Deck 9: Fundamentals of Hypothesis Testing: One-Sample Tests

Question 1

If the Type I error (α)for a given test is to be decreased,then for a fixed sample size n

A)the power of the test will increase.
B)the Type II error (β)will increase.
C)the Type II error (β)will also decrease.
D)a one-tailed test must be utilised.

Answer 1

the Type II error (β)will increase.

Question 2

For a given level of significance,if the sample size is increased,the power of the test will increase.

Answer 2

True

Question 3

For a given level of significance,if the sample size is increased,the probability of committing a Type I error will increase.

Answer 3

False

Question 4

For a given level of significance,if the sample size is increased,the probability of committing a Type II error will increase.

Question 5

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is 0.05.

Question 6

Which of the following would be an appropriate null hypothesis?

A)The mean of a sample is equal to 55.
B)The mean of a population is greater than 55.
C)The mean of a population is equal to 55.
D)Only A and C are appropriate.

Question 7

For a given sample size,the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Question 8

A region of non-rejection is sometimes called the critical region.

Question 9

A Type I error is committed when

A)we reject a null hypothesis that is false.
B)we don't reject a null hypothesis that is true.
C)we don't reject a null hypothesis that is false.
D)we reject a null hypothesis that is true.

Question 10

Which of the following would be an appropriate null hypothesis?

A)The population proportion is less than 0.65.
B)The sample proportion is no less than 0.65.
C)The sample proportion is less than 0.65.
D)The population proportion is no less than 0.65.

Question 11

If the p-value is less than α in a two-tailed test,

A)the null hypothesis should not be rejected.
B)a one-tailed test should be used.
C)no conclusion should be reached.
D)the null hypothesis should be rejected.

Question 12

If a test of hypothesis has a Type I error probability (α)of 0.01,it means that

A)if the null hypothesis is false,you reject it 1% of the time.
B)if the null hypothesis is true,you reject it 1% of the time.
C)if the null hypothesis is false,you don't reject it 1% of the time.
D)if the null hypothesis is true,you don't reject it 1% of the time.

Question 13

The power of a test is measured by its capability of

A)not rejecting a null hypothesis that is false.
B)rejecting a null hypothesis that is true.
C)rejecting a null hypothesis that is false.
D)not rejecting a null hypothesis that is true.

Question 14

Which of the following would be an appropriate alternative hypothesis?

A)The population proportion is less than 0.65.
B)The sample proportion is less than 0.65.
C)The sample proportion is no less than 0.65.
D)The population proportion is no less than 0.65.

Question 15

The statement of the null hypothesis always contains an equality.

Question 16

Which of the following would be an appropriate alternative hypothesis?

A)The mean of a sample is greater than 55.
B)The mean of a population is greater than 55.
C)The mean of a sample is equal to 55.
D)The mean of a population is equal to 55.

Question 17

A Type II error is committed when

A)we reject a null hypothesis that is true.
B)we reject a null hypothesis that is false.
C)we don't reject a null hypothesis that is true.
D)we don't reject a null hypothesis that is false.

Question 18

For a given sample size n,if the level of significance (α)is decreased,the power of the test

A)will decrease.
B)will increase.
C)will remain the same.
D)cannot be determined.

Question 19

The test statistic measures how close the computed sample statistic has come to the hypothesised population parameter.

Question 20

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.034.The null hypothesis should be rejected if the chosen level of significance is 0.01.

Question 21

The symbol for the probability of committing a Type II error of a statistical test is

A)α.
B)1 - α.
C)β.
D)1 - β.

Question 22

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what is the power of the test?

A)0.13
B)0.16
C)0.84
D)0.87

Question 23

If you know that the probability of committing a Type II error (β)is 5%,you can tell that the power of the test is

A)95%.
B)97.5%.
C)2.5%.
D)unknown.

Question 24

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

A)a one-tailed test for μ is used.
B)a two-tailed test for μ is used.
C)Both of the previous statements are true.
D)None of the previous statements are true.

Question 25

For a given level of significance (α),if the sample size n is increased,the probability of a Type II error (β)

A)will increase.
B)will decrease.
C)will remain the same.
D)cannot be determined.

Question 26

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

A)significance level
B)parameter
C)critical value
D)test statistic

Question 27

The symbol for the level of significance of a statistical test is

A)α.
B)1 - α.
C)β.
D)1 - β.

Question 28

If you know that the level of significance (α)of a test is 5%,you can tell that the probability of committing a Type II error (β)is

A)95%.
B)97.5%.
C)2.5%.
D)unknown.

Question 29

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what is the "actual confidence coefficient"?

A)0.13
B)0.16
C)0.84
D)0.87

Question 30

The power of a statistical test is

A)the probability of not rejecting H₀ when it is false.
B)the probability of rejecting H₀ when it is false.
C)the probability of not rejecting H₀ when it is true.
D)the probability of rejecting H₀ when it is true.

Question 31

If,as a result of a hypothesis test,you reject the null hypothesis when it is false,then you have committed

A)a Type II error.
B)an acceptance error.
C)a Type I error.
D)no error.

Question 32

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what is the value of β?

A)0.13
B)0.16
C)0.84
D)0.87

Question 33

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what is the value of α?

A)0.13
B)0.16
C)0.84
D)0.87

Question 34

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what would be a Type II error?

A)Saying that the person is a science student when in fact the person is a business student.
B)Saying that the person is a science student when in fact the person is a science student.
C)Saying that the person is a business student when in fact the person is a business student.
D)Saying that the person is a business student when in fact the person is a science student.

Question 35

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what would be a Type I error?

A)Saying that the person is a business student when in fact the person is a business student.
B)Saying that the person is a science student when in fact the person is a business student.
C)Saying that the person is a science student when in fact the person is a science student.
D)Saying that the person is a business student when in fact the person is a science student.

Question 36

The symbol for the power of a statistical test is

A)α.
B)1 - α.
C)β.
D)1 - β.

Question 37

The symbol for the confidence coefficient of a statistical test is

A)α.
B)1 - α.
C)β.
D)1 - β.

Question 38

Which of the following statements is NOT true about the level of significance in a hypothesis test?

A)The significance level is also called the α level.
B)The level of significance is the maximum risk we are willing to accept in making a Type I error.
C)The larger the level of significance,the more likely you are to reject the null hypothesis.
D)The significance level is another name for Type II error.

Question 39

Instruction 9-2
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
Referring to Instruction 9-2,what is the "actual level of significance" of the test?

A)0.13
B)0.16
C)0.84
D)0.87

Question 40

The symbol for the probability of committing a Type I error of a statistical test is

A)α.
B)1 - α.
C)β.
D)1 - β.

Question 41

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be accepted at a level of significance of 0.01.

Question 42

If a researcher rejects a true null hypothesis,she has made a ________ error.

Question 43

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 44

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

Question 45

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims that over the past five years,the average daily revenue was $675 with a standard deviation of $75.A sample of 30 days reveals a daily average revenue of $625.If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis,what can you conclude?

A)There is enough evidence to conclude that the daily average revenue was $675.
B)There is not enough evidence to conclude that the daily average revenue was $675.
C)There is not enough evidence to conclude that the daily average revenue was not $675.
D)There is enough evidence to conclude that the daily average revenue was not $675.

Question 46

The smaller is the p-value,the stronger is the evidence against the null hypothesis.

Question 47

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 48

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

Question 49

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be rejected at a level of significance of 0.02.

Question 50

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 51

If a researcher accepts a false null hypothesis,she has made a ________ error.

Question 52

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be rejected at a level of significance of 0.05.

Question 53

The value that separates a rejection region from a non-rejection region is called the ________.

Question 54

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18,the null hypothesis could be rejected at a level of significance of 0.05.

Question 55

If a researcher rejects a false null hypothesis,she has made a ________ decision.

Question 56

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be rejected at a level of significance of 0.10.

Question 57

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Question 58

If a researcher accepts a true null hypothesis,she has made a ________ decision.

Question 59

If an economist wishes to determine whether there is evidence that average family income in a community equals $50,000

A)a two-tailed test should be utilised.
B)either a one-tailed or two-tailed test could be used with equivalent results.
C)a one-tailed test should be utilised.
D)None of the above.

Question 60

The larger is the p-value,the more likely one is to reject the null hypothesis.

Question 61

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the p-value of the test is ________.

Question 62

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the power of the test if the mean power consumption of all such microwave ovens is in fact 248 W using a 0.05 level of significance?

Question 63

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,for this test to be valid,it is necessary that the power consumption for microwave ovens has a normal distribution.

Question 64

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the power of the test if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

Question 65

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

Question 66

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the consumer group can conclude that there is enough evidence to prove that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

Question 67

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

Question 68

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the null hypothesis will be rejected at 1% level of significance.

Question 69

Instruction 9-1
Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies:

Referring to Instruction 9-1,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

Question 70

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the population of interest is

A)the power consumption in the 20 microwave ovens.
B)the mean power consumption in the 20 microwave ovens.
C)the mean power consumption in all such microwave ovens.
D)the power consumption in all such microwave ovens.

Question 71

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are

A)H₀: μ = 250 versus H₁: μ ≠ 250.
B)H₀: μ ≤ 250 versus H₁: μ > 250.
C)H₀: μ ≥ 250 versus H₁: μ < 250.
D)H₀: μ ≥ 257.3 versus H₁: μ < 257.3.

Question 72

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the power of the test if the mean power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

Question 73

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the parameter of interest is

A)the mean power consumption of the 20 microwave ovens.
B)257.3.
C)the mean power consumption of all such microwave ovens.
D)250.

Question 74

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 248 W using a 0.05 level of significance?

Question 75

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the power of the test if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

Question 76

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

Question 77

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9.3,the value of the test statistic is ________.

Question 78

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,the null hypothesis will be rejected at 5% level of significance.

Question 79

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

Question 80

Instruction 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Referring to Instruction 9-3,for a test with a level of significance of 0.05,the critical value would be ________.