Deck 10: One-Sample Tests of Hypothesis

Question 1

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.

Answer 1

A

Question 2

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

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

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

Question 5

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

Question 6

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

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

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 9

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

Question 10

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

Question 11

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

Question 12

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 13

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

Question 14

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

Question 15

A null hypothesis makes a claim about a __________.

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

Question 16

A p-value is a probability.

Question 17

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

Question 18

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 19

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

Question 20

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 21

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

A) α
B) β
C) μ
D) z

Question 22

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 23

What is another name for the alternate hypothesis?

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

Question 24

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 25

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 26

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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 42

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 43

The average cost of tuition plus 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 44

The average cost of tuition plus 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 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

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 47

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 48

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 49

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 50

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 51

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 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 are the degrees of freedom?

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

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

The average cost of tuition plus 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 55

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.

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 mean?

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

Question 57

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 sample mean

Question 58

The average cost of tuition plus 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 59

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 60

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 61

The alternate hypothesis can be accepted only if the null hypothesis is shown to be _________.

Question 62

The Greek letter _________ is used to represent the probability of making a Type I error.

Question 63

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

A) α
B) β
C) the Type I error
D) σ

Question 64

If the null hypothesis is true and the researchers reject it, a ________ error has been made.

Question 65

A(n) ____________ hypothesis test is indicated if the alternate hypothesis states a direction.

Question 66

The p-value is determined by the value of a ______________________.

Question 67

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 68

A ____________ hypothesis test is indicated if the alternate hypothesis does not specify a direction.

Question 69

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 70

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

Question 71

If the null hypothesis is false and the researchers accept it, a _______ error has been made.

Question 72

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 73

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

Question 74

Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. In order 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 75

The z or t value that separates the region of rejection from the region of non-rejection is called a __________________.

Question 76

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 77

A statement about the value of a population parameter is called a ________________.

Question 78

In hypothesis testing, the probability of a Type I error is also called the _________________.

Question 79

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

Question 80

A manufacturer claims that less than 1% of all its products do not meet the minimum government standards. A survey of 500 products revealed that 10 did not meet the standard. The p-value is ______________.