Deck 10: One-Sample Tests of Hypothesis

Question 1

A test statistic is a value computed from sample information that is used to test the null hypothesis.

Answer 1

True

Question 2

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218, and 218. Using α = 0.025, has the shelf life of the cake mix increased?

A)Yes, because computed t is greater than the critical value.
B)Yes, because computed t is less than the critical value.
C)No, because computed t lies in the region of acceptance.
D)No, because 217.24 is quite close to 216.

Answer 2

Yes, because computed t is greater than the critical value.

Question 3

A p-value is the same as a stated significance level.

Answer 3

False

Question 4

An example of a hypothesis is: A person is innocent until proven guilty.

Question 5

A consumer products company wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. At the 0.01 level of significance, what is the decision rule to test if the new design increased the absorption of the sponge?

A)Reject null hypothesis if computed t is less than 2.580.
B)Reject null hypothesis if computed t is greater than 2.821.
C)Reject null hypothesis if computed z is 1.96 or larger.
D)Reject null hypothesis if computed t is less than 2.764.

Question 6

The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

Question 7

Define the level of significance.

A)It is the probability of a Type II error.
B)It is the probability of a Type I error.
C)It is a z value of 1.96.
D)It is the beta error.

Question 8

For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96.

Question 9

If the null hypothesis is µµ ≥ 200, then a two-tail test is being conducted.

Question 10

A null hypothesis makes a claim about a __________.

A)Population parameter
B)Sample statistic
C)Sample mean
D)Type II error

Question 11

An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.

Question 12

The mean length of a candy bar is 43 millimeters. There is concern that the settings of the machine cutting the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. The mean of the sample is 41.5 and the standard deviation is 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?

A)Yes, because the computed t lies in the rejection region.
B)No, because the information given is not complete.
C)No, because the computed t lies in the area to the right of -2.718.
D)Yes, because 43 is greater than 41.5.

Question 13

The Greek letter used to represent the probability of a Type I error is alpha (α).

Question 14

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.

Question 15

A p-value is a probability.

Question 16

If the null hypothesis is false and the researchers do not reject it, a Type I error has been made.

Question 17

A Type II error is the probability of rejecting the null hypothesis when it is actually true.

Question 18

To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is π = 0.55 and the alternate is π ≠ .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis using the 0.01 level of significance?

A)Do not reject it.
B)Reject it.
C)Cannot accept it or reject it based on the information given.
D)Purchase a condominium.

Question 19

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

Question 20

Assuming that the null hypothesis is true, a p-value is the probability of observing a sample value greater than and/or less than an observed sample observation.

Question 21

The number of trials and the population proportion are respectively represented by what symbols?

A)p and n
B)α and β
C)z and t
D)n and π

Question 22

What are the critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?

A)Above 1.960 and below -1.960
B)Above 1.645 and below -1.645
C)Above 2.576 and below -2.576
D)Above 1.000 and below -1.000

Question 23

A machine is set to fill the small-size packages of M&M candies with 56 candies per bag. A sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. To test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?

A)9
B)1
C)8
D)7

Question 24

What is another name for the alternate hypothesis?

A)Null hypothesis
B)Hypothesis of no difference
C)Rejected hypothesis
D)Research hypothesis

Question 25

For a one-tailed hypothesis test, the critical z value of the test statistic is -2.33. Which of the following is true about the hypothesis test?

A)α = 0.05 for a lower-tailed test
B)α = 0.01 for a lower-tailed test
C)α = 0.05 for an upper-tailed test
D)α = 0.01 for an upper-tailed test

Question 26

Which symbol represents a test statistic used to test a hypothesis about a population mean?

A)α
B)β
C)μ
D)z

Question 27

What statement do we make that determines if the null hypothesis is rejected?

A)Decision rule
B)Test statistic
C)Alternate hypothesis
D)Critical value

Question 28

For a two-tailed test with a 0.05 significance level, where is the rejection region when n is large and the population standard deviation is known?

A)Between ±1.960
B)Between ±1.645
C)Greater than +1.960 and less than -1.960
D)Greater than +1.645 and less than -1.645

Question 29

What is a Type II error?

A)Failing to reject a false null hypothesis
B)Rejecting a false null hypothesis
C)Accepting a false alternate hypothesis
D)Rejecting a false alternate hypothesis

Question 30

If we reject the null hypothesis, what can we conclude subject to the probability, α?

A)Reject the null with a probability, α, of making a Type I error.
B)The alternative hypothesis is false.
C)The null hypothesis is true.
D)Both the null hypothesis and the alternative hypothesis are true.

Question 31

If the alternate hypothesis states that µ ≠ 4,000, where is the rejection region for the hypothesis test?

A)In both tails
B)In the lower or left tail
C)In the upper or right tail
D)In the center

Question 32

What is the probability of making a Type II error if the null hypothesis is actually true?

A)α
B)1
C)0
D)0.05

Question 33

For an alternative hypothesis: µ > 6,700, where is the rejection region for the hypothesis test located?

A)In both tails
B)In the left or lower tail
C)In the right or upper tail
D)In the center

Question 34

For a null hypothesis, H₀: µ = 4,000, if the 1% level of significance is used and the z-test statistic is +6.00, what is our decision regarding the null hypothesis?

A)Do not reject H₀.
B)Reject H₀.
C)Reject H₁.
D)None Apply.

Question 35

If the critical z value for a hypothesis test equals 2.45, what value of the test statistic would provide the least chance of making a Type I error?

A)3.74
B)10,000
C)2.46
D)4.56

Question 36

Using a 5% level of significance and a sample size of 25, what is the critical t value for a null hypothesis, H₀: µµ ≤ 100?

A)1.708
B)1.711
C)2.060
D)2.064

Question 37

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?

A)To the left of -1.282 or to the right of 1.282
B)To the left of -1.345 or to the right of 1.345
C)Between -1.761 and 1.761
D)To the left of -1.645 or to the right of 1.645

Question 38

To conduct a test of hypothesis with a small sample, we make an assumption that __________.

A)A larger computed value of t will be needed to reject the null hypothesis
B)The region of acceptance will be wider than for large samples
C)The confidence interval will be wider than for large samples
D)The population is normally distributed

Question 39

What are the critical z-values for a two-tailed hypothesis test if α = 0.01?

A)±1.960
B)±2.326
C)±2.576
D)±1.645

Question 40

Which of the following is NOT one of the five steps in the hypothesis testing procedure?

A)Formulate a decision rule
B)State the null and alternate hypotheses
C)Select a level for β
D)Identify the test statistic

Question 41

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What are the null and alternative hypotheses for this study?

A)H₀: µ ≤ $9,000; H₁: µ > $9,000
B)H₀: µ ≥ $9,000; H₁: µ < $9,000
C)H₀: µ ≤ $8,500; H₁: µ > $8,500
D)H₀: µ ≥ $8,500; H₁: µ < $8,500

Question 42

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the test statistic for this test?

A)±3.82
B)+0.204
C)-3.82
D)+3.82

Question 43

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if α = 0.01?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the newscast does not reach 41% of the audience.
C)Fail to reject the alternate and conclude the newscast does not reach 41% of the audience.
D)Reject the alternate and conclude the newscast reaches about 41% of the audience.

Question 44

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z value for this test?

A)+1.960
B)-1.960
C)+1.645
D)-1.645

Question 45

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?

A)0.41
B)0.36%
C)0.41%
D)0.36

Question 46

If 20 out of 50 students sampled live in a college dormitory, what is the estimated proportion of students at the University living in a dormitory?

A)0.20
B)0.40
C)0.50
D)0.60

Question 47

The sample proportion is defined as _________.

A)nπ
B)x/n
C)n!
D)π

Question 48

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the z test statistic?

A)1.02
B)1.22
C)-1.02
D)-1.22

Question 49

The average cost of tuition and room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the p-value for this test?

A)0.0000
B)0.0124
C)0.0500
D)0.4938

Question 50

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the null hypothesis?

A)H₀: π = 0.36
B)H₀: π = 0.41
C)H₀: π ≠ 0.36
D)H₀: µ = 0.41

Question 51

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the alternate hypothesis for a one-sided test?

A)H₁: π ≥ 0.10
B)H₁: π > 0.10
C)H₁: π ≤ 0.10
D)H₁: π < 0.10

Question 52

An electronics retailer believes that, at most, 40% of their cell phone inventory was sold during November. The retailer surveyed 80 dealers and found that 38% of the inventory was sold. Since 38% is less than 40%, is this difference of 2 percentage points sampling error or a significant difference? Test at the 0.05 level. The computed z = -0.37.

A)The 2% is a significant difference.
B)We cannot determine if the 2% is a significant difference.
C)There is not enough information to reach a conclusion.
D)None Apply.

Question 53

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the p-value?

A)0.3461
B)0.1539
C)0.3078
D)0.0100

Question 54

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if the level of significance is 0.10?

A)-1.282
B)±1.645
C)-2.576
D)+2.576

Question 55

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the null hypothesis?

A)H₀: π ≠ 0.10
B)H₀: π ≥ 0.10
C)H₀: π ≤ 0.10
D)H₀: π < 0.10

Question 56

The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 significance level. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

A)Do not reject the null hypothesis because -0.879 lies in the region between +2.326 and -2.326.
B)Do not reject the null hypothesis because -0.879 lies in the region between +2.5760 and -2.576.
C)Reject the null hypothesis because 37% is less than 40%.
D)Do not reject the null hypothesis because 37% lies in the area between 0% and 40%.

Question 57

In hypothesis testing, what is the level of significance?

A)The risk of rejecting the null hypothesis when it is true.
B)A value symbolized by the Greek letter α.
C)A value between 0 and 1.
D)It is selected before a decision rule can be formulated.
E)All apply.

Question 58

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the alternate hypothesis?

A)H₁: π = 0.36
B)H₁: π = 0.41
C)H₁: π ≠ 0.41
D)H₁: µ ≠ 0.41

Question 59

Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if α = 0.01?

A)+2.576
B)+2.326
C)±2.576
D)-2.326

Question 60

The average cost of tuition and room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?

A)Equal to $8,500
B)Greater than $8,500
C)Less than $8,500
D)Not equal to $8,500

Question 61

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample variance?

A)1.177
B)6.6
C)1.385
D)7.6

Question 62

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?

A)0.10
B)0.125
C)40
D)0.40

Question 63

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample standard deviation?

A)1.177
B)1.188
C)1.386
D)1.090

Question 64

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule?

A)Do not reject the null hypothesis if computed z lies between -1.645 and +1.645; otherwise, reject it.
B)Do not reject the null hypothesis if computed z is greater than 1.645; otherwise, reject it.
C)Do not reject the null hypothesis if computed z lies between -1.960 and +1.960; otherwise, reject it.
D)Reject the null hypothesis if computed z is below -1.960; otherwise, reject it.

Question 65

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What are the degrees of freedom?

A)7
B)8
C)6
D)6.6

Question 66

The critical t statistic for an alternative hypothesis, H₁: µ > 30, a 1% level of significance, and a sample size of 8 is __________.

Question 67

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the alternate hypothesis?

A)H₁: µ = 6.6
B)H₁: µ ≠ 6.6
C)H₁: µ ≥ 6.6
D)H₁: µ > 7.6

Question 68

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the critical value for α = 0.025?

A)+1.960
B)±1.645
C)-1.960
D)-1.645

Question 69

The critical t statistic for the alternative hypothesis, H₁: µ < 12, a 0.005 level of significance, and a sample size of 20 is ______.

Question 70

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. Which of the following is the alternate hypothesis?

A)H₁: π ≠ $50,000
B)H₁: µ ≠ $50,000
C)H₁: µ < $50,000
D)H₁: µ = $50,000

Question 71

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than 6.6 lb.
C)Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
D)Cannot calculate because the population standard deviation is unknown.

Question 72

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. The null hypothesis is ______.

A)H₀: µ = 6.6
B)H₀: µ ≥ 6.6
C)H₀: µ > 7.6
D)H₀: µ ≤ 7.6

Question 73

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the p-value?

A)0.0250
B)0.4525
C)0.9525
D)0.0500

Question 74

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the critical value?

A)+1.645
B)-1.282
C)±1.282
D)±1.645

Question 75

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. If α = 0.05, what is the critical t value?

A)-2.365
B)±1.96
C)±2.365
D)±2.447

Question 76

As the sample size increases, the curve of the t-distribution approaches the _____________________________.

Question 77

A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

A)6.6
B)7.6
C)1.177
D)2.447

Question 78

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. If α = 0.025, what will be the decision?

A)Accept the null.
B)Reject the null and conclude the defects are not greater than 10%.
C)Reject the null and conclude the defects are greater than 10%.
D)Fail to reject the null.

Question 79

It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-test statistic?

A)+0.125
B)+0.278
C)-1.645
D)+1.667

Question 80

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?

A)Fail to reject the null hypothesis and conclude the mean is 6.6 lb.
B)Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
C)Reject the null hypothesis and conclude the mean is greater than 6.6 lb.
D)Cannot calculate because the population standard deviation is unknown.