Deck 10: One-Sample Tests of Hypothesis

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

Assuming that the null hypothesis is true,a p-value is the probability of observing a sample value as extreme as,or more extreme than,the observed sample observation.

Question 5

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 6

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 7

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

Question 8

A null hypothesis makes a claim about a ________.

A)population parameter
B)sample statistic
C)sample mean
D)type II error

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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 in millimeters recorded. The lengths (in millimeters)are 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. If the 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 14

The probability of a Type II error is represented by the Greek symbol β.

Question 15

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.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

A p-value is a probability.

Question 21

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 22

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 of the answers apply.

Question 23

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 24

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 25

What is another name for the alternate hypothesis?

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

Question 26

Which of the following is not one of the six 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 27

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 28

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

A)α
B)β
C)μ
D)z

Question 29

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 30

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 31

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)1.07
C)2.46
D)4.56

Question 32

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 of these answers apply.

Question 33

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

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

Question 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

The average cost of tuition plus room and board at for 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 42

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 43

The mean annual incomes of certified welders are normally distributed with the 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. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.10,what conclusion should be drawn?

A)Do not reject the null hypothesis as the test statistic is less than the critical value of z.
B)Do not reject the null hypothesis as the test statistic is less than the critical value of t.
C)Reject the null hypothesis as the test statistic is greater than the critical value of t.
D)Reject the null hypothesis as the test statistic is greater than the critical value of z.

Question 44

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 45

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 46

The mean annual incomes of certified welders are normally distributed with the 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 critical value?

A)+1.645
B)−1.282
C)±1.282
D)±1.645

Question 47

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 48

The average cost of tuition and room and board for 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 49

The average cost of tuition plus room and board for 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 50

The mean annual incomes of certified welders are normally distributed with the 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. A sample of 100 welders is taken and the mean annual income of the sample is $50,350. If the level of significance is 0.05,what conclusion should be drawn?

A)Do not reject the null hypothesis as the test statistic is less than the critical value of z.
B)Do not reject the null hypothesis as the test statistic is less than the critical value of t.
C)Reject the null hypothesis as the test statistic is greater than the critical value of t.
D)Reject the null hypothesis as the test statistic is greater than the critical value of z.

Question 51

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 52

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)1.386
D)7.6

Question 53

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 pounds.
C)Reject the null hypothesis and conclude the mean is lower than 6.6 pounds.
D)Cannot calculate because the population standard deviation is unknown.

Question 54

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

Question 55

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 56

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 57

The average cost of tuition plus room and board for 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 p-value for this test?

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

Question 58

The average cost of tuition plus room and board for 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. 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 59

The probability of a Type II error is directly related to ________.

A)α
B)the standard deviation
C)the Type I error
D)the difference between the hypothesized mean and the critical value of the sample mean

Question 60

The mean annual incomes of certified welders are normally distributed with the 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. Which of the following is the alternate hypothesis?

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

Question 61

Consider a left-tailed test,where the p-value is found to be 0.10. If the sample size n for this test is 49,then the t-statistic will have a value of ________.

A)+1.677
B)−1.677
C)+1.299
D)−1.299

Question 62

The probability of a Type II error is represented by ________.

A)α
B)β
C)the Type I error
D)σ

Question 63

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,400 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. The value of the test statistic is ________.

A)2.8
B)6,000
C)6,400
D)1.96

Question 64

Consider a two-tailed test with a level of confidence of 80.30%. The z-value is ________.

A)2.58
B)1.29
C)0.85
D)1.96

Question 65

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.025,have sales increased as a result of the advertising campaign?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

Question 66

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05; therefore,the null hypothesis ________.

A)should not be rejected
B)must be rejected
C)may or may not be rejected depending on the square root of the sample size
D)is the same as the alternative hypothesis

Question 67

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.05,have sales increased as a result of the advertising campaign?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

Question 68

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.01,have sales increased as a result of the advertising campaign?

A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.

Question 69

Consider a right-tailed test (upper tail)and a sample size of 40 at the 95% confidence level. The value of t is ________.

A)+2.023
B)−2.023
C)−1.685
D)+1.685