Deck 9: Hypothesis Tests About the Mean and Proportion

Question 1

In a two-tailed hypothesis test,the two critical points are the points that divide the area under the sampling distribution of a:

A)statistic into two rejection regions and one nonrejection region
B)parameter into one rejection region and one nonrejection region
C)statistic into one rejection region and two nonrejection regions
D)parameter into two rejection regions and one nonrejection region

Answer 1

statistic into two rejection regions and one nonrejection region

Question 2

In a hypothesis test,a Type I error occurs when:

A)a false null hypothesis is rejected
B)a true null hypothesis is not rejected
C)a false null hypothesis is not rejected
D)a true null hypothesis is rejected

Answer 2

a true null hypothesis is rejected

Question 3

The alternative hypothesis is a claim about a:

A)parameter,where the claim is assumed to be true until it is declared false
B)parameter,where the claim is assumed to be true if the null hypothesis is declared false
C)statistic,where the claim is assumed to be true if the null hypothesis is declared false
D)statistic,where the claim is assumed to be false until it is declared true

Answer 3

parameter,where the claim is assumed to be true if the null hypothesis is declared false

Question 4

A two-tailed hypothesis test contains:

A)one rejection region and two nonrejection regions
B)two rejection regions and one nonrejection region
C)two rejection regions and two nonrejection regions
D)one rejection region and one nonrejection region

Question 5

A researcher wants to test if the mean annual salary of all lawyers in a city is different than $110,000.The null hypothesis for this example will be that the population mean is:

A)equal to $110,000
B)less than to $110,000
C)not equal to $110,000
D)greater than $110,000

Question 6

The p-value is the:

A)largest significance level at which the null hypothesis can be rejected
B)largest significance level at which the alternative hypothesis can be rejected
C)smallest significance level at which the null hypothesis can be rejected
D)smallest significance level at which the alternative hypothesis can be rejected

Question 7

In a two-tailed hypothesis test,the sign in the alternative hypothesis is:

A)not equal to
B)greater than
C)less than
D)less than or equal to

Question 8

In a right-tailed hypothesis test,the sign in the alternative hypothesis is:

A)not equal to
B)greater than
C)less than
D)less than or equal to

Question 9

A researcher wants to test if elementary school children spend less than 30 minutes per day on homework.The alternative hypothesis for this example will be that the population mean is:

A)equal to 30 minutes
B)not equal to 30 minutes
C)less than or equal to 30 minutes
D)less than 30 minutes

Question 10

A one-tailed hypothesis test contains:

A)one rejection region and two nonrejection regions
B)two rejection regions and one nonrejection region
C)two rejection regions and two nonrejection regions
D)one rejection region and one nonrejection region

Question 11

In a one-tailed hypothesis test,a critical point is a point that divides the area under the sampling distribution of a:

A)statistic into one rejection region and one nonrejection region
B)parameter into one rejection region and one nonrejection region
C)statistic into one rejection region and two nonrejection regions
D)parameter into two rejection regions and one nonrejection region

Question 12

In a hypothesis test,a Type II error occurs when:

A)a false null hypothesis is rejected
B)a true null hypothesis is not rejected
C)a false null hypothesis is not rejected
D)a true null hypothesis is rejected

Question 13

The null hypothesis is a claim about a:

A)parameter,where the claim is assumed to be false until it is declared true
B)parameter,where the claim is assumed to be true until it is declared false
C)statistic,where the claim is assumed to be false until it is declared true
D)statistic,where the claim is assumed to be true until it is declared false

Question 14

A researcher wants to test if the mean price of houses in an area is greater than $145,000.The alternative hypothesis for this example will be that the population mean is:

A)equal to $145,000
B)not equal to $145,000
C)greater than or equal to $145,000
D)greater than $145,000

Question 15

A researcher wants to test if elementary school children spend less than 30 minutes per day on homework.The null hypothesis for this example will be that the population mean is:

A)greater than or equal to 30 minutes
B)not equal to 30 minutes
C)less than or equal to 30 minutes
D)less than 30 minutes

Question 16

A researcher wants to test if the mean annual salary of all lawyers in a city is different than $110,000.The alternative hypothesis for this example will be that the population mean is:

A)equal to $110,000
B)less than to $110,000
C)not equal to $110,000
D)greater than $110,000

Question 17

A researcher wants to test if the mean price of houses in an area is greater than $175,000.The null hypothesis for this example will be that the population mean is:

A)less than or equal to $175,000
B)not equal to $175,000
C)greater than or equal to $175,000
D)greater than $175,000

Question 18

In a left-tailed hypothesis test,the sign in the alternative hypothesis is:

A)not equal to
B)greater than
C)less than
D)less than or equal to

Question 19

In a hypothesis test,the probability of committing a Type I error is called the:

A)confidence level
B)confidence interval
C)significance level
D)beta error

Question 20

For a one-tailed test,the p-value is:

A)the area under the curve between the mean and the observed value of the sample statistic
B)twice the area under the curve between the mean and the observed value of the sample statistic
C)the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis
D)twice the area under the curve to the same side of the value of the sample statistic as is specified in the alternative hypothesis

Question 21

In a hypothesis test with hypotheses and ,a random sample of 131 elements selected from the population produced a mean of 131.6.Assuming that 18.8,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 22

Use the following to answer questions :
A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000.A random sample of 53 lawyers selected from the city reveals a mean annual salary of $114,000.Assume that $17,000,and that the test is to be made at the 1% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 23

Use the following to answer questions :
A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000.A random sample of 53 lawyers selected from the city reveals a mean annual salary of $114,000.Assume that $17,000,and that the test is to be made at the 1% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 24

Use the following to answer questions : In a hypothesis test with hypotheses H₀ : μ=90 and H₁ : μ ≠ 90 , a random sample of 103 elements selected from the population produced a mean of 94.3. Assume that σ = 22.1, and that the test is to be made at the 5% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 25

Use the following to answer questions : In a hypothesis test with hypotheses H₀ : μ=90 and H₁ : μ ≠ 90 , a random sample of 103 elements selected from the population produced a mean of 94.3. Assume that σ = 22.1, and that the test is to be made at the 5% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 26

In a hypothesis test with hypotheses and ,a random sample of 59 elements selected from the population produced a mean of 35.8.Assuming that 9.9,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 27

Use the following to answer questions :
A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework.A random sample of 64 children from the school shows that they spend an average of 24.5 minutes per day on homework.Assume that 15.3 minutes,and that the test is to be made at the 1% significance level.
What is the critical value of z?

A)-2.06
B)-2.33
C)-2.58
D)-1.96

Question 28

Use the following to answer questions :
A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000.A random sample of 53 lawyers selected from the city reveals a mean annual salary of $114,000.Assume that $17,000,and that the test is to be made at the 1% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 29

Use the following to answer questions :
A researcher wants to test if the mean price of houses in an area is greater than $145,000.A random sample of 35 houses selected from the area produces a mean price of $149,700.Assume that $13,100,and that the test is to be made at the 1% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 30

In a hypothesis test with hypotheses and ,a random sample of 100 elements selected from the population produced a mean of 137.0.Assuming that 28.1,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 31

In a hypothesis test with hypotheses and ,a random sample of 38 elements selected from the population produced a mean of 74.4.Assuming that 8.9 and the population is normally distributed,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 32

Use the following to answer questions :
A researcher wants to test if the mean price of houses in an area is greater than $145,000.A random sample of 35 houses selected from the area produces a mean price of $149,700.Assume that $13,100,and that the test is to be made at the 1% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 33

In a hypothesis test with hypotheses and ,a random sample of 37 elements selected from the population produced a mean of 62.5.Assuming that 5.2 and the population is normally distributed,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 34

Use the following to answer questions : In a hypothesis test with hypotheses H₀ : μ=90 and H₁ : μ ≠ 90 , a random sample of 103 elements selected from the population produced a mean of 94.3. Assume that σ = 22.1, and that the test is to be made at the 5% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 35

Use the following to answer questions :
A researcher wants to test if the mean price of houses in an area is greater than $145,000.A random sample of 35 houses selected from the area produces a mean price of $149,700.Assume that $13,100,and that the test is to be made at the 1% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 36

Use the following to answer questions :
A researcher wants to test if the mean price of houses in an area is greater than $145,000.A random sample of 35 houses selected from the area produces a mean price of $149,700.Assume that $13,100,and that the test is to be made at the 1% significance level.
What is the critical value of z?

A)1.88
B)2.17
C)1.96
D)2.58

Question 37

Suppose that the batting average for all major league baseball players after each team completes 100 games through the season is 0.248 and the standard deviation is 0.034.The null hypothesis is that American League infielders average the same as all other major league players.A sample of 46 players taken from the American League reveals a mean batting average of 0.255.What is the value of the test statistic,z (rounded to two decimal places)?

Question 38

For a two-tailed test,the p-value is:

A)the area under the curve between the mean and the observed value of the sample statistic
B)twice the area under the curve between the mean and the observed value of the sample statistic
C)the area in the tail under the curve on the side which the sample statistic lies
D)twice the area in the tail under the curve on the side which the sample statistic lies

Question 39

In a hypothesis test with hypotheses and ,a random sample of 61 elements selected from the population produced a mean of 90.7.Assuming that 29.8,what is the approximate p-value for this test? (round your answer to four decimal places)

Question 40

Use the following to answer questions :
A researcher wants to test if the mean annual salary of all lawyers in a city is different from $110,000.A random sample of 53 lawyers selected from the city reveals a mean annual salary of $114,000.Assume that $17,000,and that the test is to be made at the 1% significance level.
What are the critical values of z?

A)-1.96 and 1.96
B)-2.58 and 2.58
C)-2.33 and 2.33
D)-2.05 and 2.05

Question 41

Use the following to answer questions :
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours.A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours and a standard deviation of 133 hours.A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours.The significance level is 5%.Assume the population is normally distributed.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 42

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 20 elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.The significance level is 5%.Assume the population is normally distributed.
What is the value of the test statistic,t,rounded to three decimal places?

Question 43

Use the following to answer questions :
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours.A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours and a standard deviation of 133 hours.A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours.The significance level is 5%.Assume the population is normally distributed.
What is the critical value of t?

A)-1.704
B)-1.711
C)-2.797
D)-2.787

Question 44

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.The test is to be made at the 10% significance level.Assume the population is normally distributed.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 45

Which of the following conditions is not required to use the t distribution to perform a hypothesis test about a population mean?

A)The population from which the sample is drawn is approximately normal
B)The population from which the sample is drawn has a t distribution
C)The population standard deviation is unknown
D)The sample does not have any extreme outliers

Question 46

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 16 elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.The test is to be made at the 2% significance level.Assume the population is normally distributed.
What is the value of the test statistic,t,rounded to three decimal places?

Question 47

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 16 elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.The test is to be made at the 2% significance level.Assume the population is normally distributed.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 48

Use the following to answer questions :
A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework.A random sample of 64 children from the school shows that they spend an average of 24.5 minutes per day on homework.Assume that 15.3 minutes,and that the test is to be made at the 1% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 49

We use the t distribution to perform a hypothesis test about the population mean when:

A)the population from which the sample is drawn is approximately normal and the population standard deviation is known
B)the population from which the sample is drawn is not approximately normal and the population standard deviation is known
C)the population from which the sample is drawn is approximately normal and the population standard deviation is unknown
D)the population from which the sample is drawn is not approximately normal and the population standard deviation is unknown

Question 50

Use the following to answer questions :
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours.A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours and a standard deviation of 133 hours.A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours.The significance level is 5%.Assume the population is normally distributed.
What is the value of the test statistic,t,rounded to three decimal places?

Question 51

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 16 elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.The test is to be made at the 2% significance level.Assume the population is normally distributed.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 52

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 20 elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.The significance level is 5%.Assume the population is normally distributed.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 53

Use the following to answer questions :
A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework.A random sample of 64 children from the school shows that they spend an average of 24.5 minutes per day on homework.Assume that 15.3 minutes,and that the test is to be made at the 1% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 54

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.The test is to be made at the 10% significance level.Assume the population is normally distributed.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 55

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 20 elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.The significance level is 5%.Assume the population is normally distributed.
What is the critical value of t?

A)-1.645
B)-1.725
C)-1.729
D)-2.093

Question 56

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.The test is to be made at the 10% significance level.Assume the population is normally distributed.
What is the value of the test statistic,t,rounded to three decimal places?

Question 57

Use the following to answer questions :
A researcher wants to test if the elementary school children spend less than 30 minutes per day on homework.A random sample of 64 children from the school shows that they spend an average of 24.5 minutes per day on homework.Assume that 15.3 minutes,and that the test is to be made at the 1% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 58

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 20 elements selected from the population produced a mean of 67.8 and a standard deviation of 11.9.The significance level is 5%.Assume the population is normally distributed.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 59

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 24 elements selected from the population produced a mean of 58.6 and a standard deviation of 13.4.The test is to be made at the 10% significance level.Assume the population is normally distributed.
What is the critical value of t?

A)1.318
B)1.28
C)-1.319
D)1.319

Question 60

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of 16 elements selected from the population produced a mean of 91.9 and a standard deviation of 4.9.The test is to be made at the 2% significance level.Assume the population is normally distributed.
What are the critical values of t?

A)-2.33 and 2.33
B)-2.602 and 2.602
C)-2.131 and 2.131
D)-2.583 and 2.583

Question 61

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 1,165 produced a sample proportion of 0.6160.The test is to be made at the 2.5% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 62

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 974 produced a sample proportion of 0.7380.The test is to be made at the 5% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 63

Does the data provide evidence to contradict the company's claim about the average lifetime of their light bulbs? (State your answer as "no" or "yes",but don't include the quotation marks.)

Question 64

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 530 produced a sample proportion of 0.2755.The test is to be made at the 2% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 65

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 974 produced a sample proportion of 0.7380.The test is to be made at the 5% significance level.
What is the critical value of z?

A)-2.05
B)-2.33
C)-1.96
D)-1.65

Question 66

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 809 produced a sample proportion of 0.2400.The test is to be made at the 5% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 67

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 1,165 produced a sample proportion of 0.6160.The test is to be made at the 2.5% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 68

Use the following to answer questions :
A company that manufactures light bulbs claims that its light bulbs last an average of 1,150 hours.A sample of 25 light bulbs manufactured by this company gave a mean life of 1,097 hours and a standard deviation of 133 hours.A consumer group wants to test the hypothesis that the mean life of light bulbs produced by this company is less than 1,150 hours.The significance level is 5%.Assume the population is normally distributed.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 69

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 481 produced a sample proportion of 0.4350.The test is to be made at the 5% significance level.
What is the p-value for this hypothesis test,rounded to four decimal places?

Question 70

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 481 produced a sample proportion of 0.4350.The test is to be made at the 5% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 71

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 1,165 produced a sample proportion of 0.6160.The test is to be made at the 2.5% significance level.
What is the critical value of z?

A)1.65
B)2.33
C)1.96
D)2.58

Question 72

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 481 produced a sample proportion of 0.4350.The test is to be made at the 5% significance level.
What is the critical value of z?

A)1.96
B)1.645
C)2.12
D)2.72

Question 73

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 809 produced a sample proportion of 0.2400.The test is to be made at the 5% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 74

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 809 produced a sample proportion of 0.2400.The test is to be made at the 5% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 75

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 481 produced a sample proportion of 0.4350.The test is to be made at the 5% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)

Question 76

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 530 produced a sample proportion of 0.2755.The test is to be made at the 2% significance level.
What is the critical value of z?

A)-2.33
B)-2.05
C)-1.645
D)-1.714

Question 77

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 809 produced a sample proportion of 0.2400.The test is to be made at the 5% significance level.
What are the critical values of z?

A)-2.58 and 2.58
B)-1.645 and 1.645
C)-1.96 and 1.96
D)-1.72 and 1.72

Question 78

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 1,165 produced a sample proportion of 0.6160.The test is to be made at the 2.5% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 79

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 974 produced a sample proportion of 0.7380.The test is to be made at the 5% significance level.
What is the value of the test statistic,z,rounded to three decimal places?

Question 80

Use the following to answer questions :
In a hypothesis test with hypotheses and ,a random sample of size 974 produced a sample proportion of 0.7380.The test is to be made at the 5% significance level.
Should you reject or fail to reject the null hypothesis in this test? (State your answer as "reject" or "fail to reject",but don't include the quotation marks.)