Deck 9: Hypothesis Tests

Question 1

Which of the following is an improper form of the null and alternative hypotheses?

A) $H _ { 0 } : \mu \leq \mu _ { 0 }$ and $H _ { a } : \mu > \mu _ { 0 }$
B) $H _ { 0 } : \mu = \mu _ { 0 }$ and $H _ { a } : \mu \neq \mu _ { 0 }$
C) $H _ { 0 } : \mu < \mu _ { 0 }$ and $H _ { a } : \mu \geq \mu _ { 0 }$
D) $H _ { 0 } : \mu \geq \mu _ { 0 }$ and $H _ { a } : \mu < \mu _ { 0 }$

Answer 1

$H _ { 0 } : \mu < \mu _ { 0 }$ and $H _ { a } : \mu \geq \mu _ { 0 }$

Question 2

Which of the following hypotheses is not a valid null hypothesis?

A) H0: μ ≤ 0
B) H0: μ ≥ 0
C) H0: μ = 0
D) H0: μ < 0

Answer 2

H0: μ < 0

Question 3

As a general guideline, the research hypothesis should be stated as the _____.

A) null hypothesis
B) alternative hypothesis
C) tentative assumption
D) hypothesis the researcher wants to disprove

Answer 3

alternative hypothesis

Question 4

The average life expectancy of tires produced by Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is _____.

A) H0: μ < 40,000 H_a: μ ≥ 40,000
B) H0: μ ≤ 40,000 H_a: μ > 40,000
C) H0: μ > 40,000 H_a: μ ≤ 40,000
D) H0: μ ≥ 40,000 H_a: μ < 40,000

Question 5

A Type I error is committed when _____.

A) a true alternative hypothesis is not accepted
B) a true null hypothesis is rejected
C) the critical value is greater than the value of the test statistic
D) sample data contradict the null hypothesis

Question 6

More evidence against H₀ is indicated by _____.

A) lower levels of significance
B) smaller p-values
C) smaller critical values
D) lower probabilities of a Type II error

Question 7

If the cost of a Type I error is high, a smaller value should be chosen for the _____.

A) critical value
B) confidence coefficient
C) level of significance
D) test statistic

Question 8

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____.

A) less than or equal to the critical value
B) less than or equal to the test statistic
C) greater than or equal to the critical value
D) greater than or equal to the test statistic

Question 9

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is _____.

A) H₀: μ < 12 H_a: μ ≤ 12
B) H₀: μ ≤ 12 H_a: μ > 12
C) H₀: μ ≠ 12 H_a: μ = 12
D) H₀: μ = 12 H_a: μ ≠ 12

Question 10

The practice of concluding "do not reject H₀" is preferred over "accept H₀" when we _____.

A) are conducting a one-tailed test
B) are testing the validity of a claim
C) have an insufficient sample size
D) have not controlled for the Type II error

Question 11

The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is _____.

A) H₀: μ < 5 H_a: μ ≤ 5
B) H₀: μ ≤ 5 H_a: μ > 5
C) H₀: μ > 5 H_a: μ ≤ 5
D) H₀: μ ≥ 5 H_a: μ < 5

Question 12

A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is _____.

A) H₀: μ < 80 H_a: μ ≤ 80
B) H₀: μ ≤ 80 H_a: μ > 80
C) H₀: μ ≠ 80 H_a: μ = 80
D) H₀: μ = 80 H_a: μ ≠ 80

Question 13

In hypothesis testing, the hypothesis tentatively assumed to be true is _____.

A) the alternative hypothesis
B) the null hypothesis
C) either the null or the alternative
D) None of the answers is correct.

Question 14

In tests about a population proportion, p₀ represents the _____.

A) hypothesized population proportion
B) observed sample proportion
C) observed p-value
D) probability of $p - \bar { p } = 0$

Question 15

An example of statistical inference is _____.

A) a population mean
B) descriptive statistics
C) calculating the size of a sample
D) hypothesis testing

Question 16

Two approaches to drawing a conclusion in a hypothesis test are _____.

A) p-value and critical value
B) one-tailed and two-tailed
C) Type I and Type II
D) null and alternative

Question 17

In hypothesis testing, the alternative hypothesis is _____.

A) the hypothesis tentatively assumed true in the hypothesis-testing procedure
B) the hypothesis concluded to be true if the null hypothesis is rejected
C) the maximum probability of a Type I error
D) All of the answers are correct.

Question 18

For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____.

A) confidence interval estimate of μ; hypothesized value of μ
B) p-value; value of α
C) value of the test statistic; critical value
D) level of significance; confidence coefficient

Question 19

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is _____.

A) H₀: μ < 85 H_a: μ ≥ 85
B) H₀: μ ≤ 85 H_a: μ > 85
C) H₀: μ ≥ 85 H_a: μ < 85
D) H₀: μ > 85 H_a: μ ≤ 85

Question 20

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____.

A) H₀: μ < 10.0% H_a: μ ≥ 10.0%
B) H₀: μ ≤ 10.0% H_a: μ > 10.0%
C) H₀: μ > 10.0% H_a: μ ≤ 10.0%
D) H₀: μ ≥ 10.0% H_a: μ < 10.0%

Question 21

The probability of making a Type I error is denoted by _____.

A) α
B) β
C) 1 − α
D) 1 − β

Question 22

The level of significance is the _____.

A) maximum allowable probability of a Type II error
B) maximum allowable probability of a Type I error
C) same as the confidence coefficient
D) same as the p-value

Question 23

The error of rejecting a true null hypothesis is _____.

A) a Type I error
B) a Type II error
C) either a Type I or Type II error, depending on the situation
D) committed when not enough information is available

Question 24

In hypothesis testing if the null hypothesis is rejected, _____.

A) no conclusions can be drawn from the test
B) the alternative hypothesis must also be rejected
C) the data must have been collected incorrectly
D) the evidence supports the alternative hypothesis

Question 25

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (lower tail) at a .063 level of significance; z = _____.

A) -1.86
B) -1.53
C) -1.96
D) -1.645

Question 26

When the hypotheses H₀: μ ≥ 100 and H_a: μ < 100 are being tested at a level of significance of α, the null hypothesis will be rejected if the test statistic z is _____.

A) > zα
B) > -zα
C) < -zα
D) < 100

Question 27

For a two-tailed test with a sample size of 40, the null hypothesis will NOT be rejected at a 5% level of significance if the test statistic is _____.

A) between -1.96 and 1.96, exclusively
B) greater than 1.96
C) less than 1.645
D) greater than -1.645

Question 28

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true, _____.

A) a Type I error has been committed
B) a Type II error has been committed
C) either a Type I or Type II error has been committed
D) the correct decision has been made

Question 29

The level of significance is symbolized by _____.

A) $\alpha$
B) $\beta$
C) ?
D) p

Question 30

For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is _____.

A) less than or equal to -1.645
B) greater than or equal to 1.645
C) less than 1.645
D) less than -1.96

Question 31

The level of significance in hypothesis testing is the probability of _____.

A) accepting a true null hypothesis
B) accepting a false null hypothesis
C) rejecting a true null hypothesis
D) accepting a true null hypothesis, accepting a false null hypothesis, or rejecting a true null hypothesis, depending on the situation

Question 32

In order to test the hypotheses H₀: μ ≤ 100 and H_a: μ > 100 at an α level of significance, the null hypothesis will be rejected if the test statistic z is _____.

A) ≥ zα
B) < zα
C) ≤ -zα
D) < 100

Question 33

A Type II error is committed when _____.

A) a true alternative hypothesis is mistakenly rejected
B) a true null hypothesis is mistakenly rejected
C) the sample size has been too small
D) not enough information has been available

Question 34

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at a .123 level of significance; z = _____.

A) 1.54
B) 1.96
C) 1.645
D) 1.16

Question 35

Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test at a .0694 level of significance; z = _____.

A) -1.96 and 1.96
B) -1.48 and 1.48
C) -1.09 and 1.09
D) -.86 and .86

Question 36

In the hypothesis testing procedure, α is _____.

A) the level of significance
B) the critical value
C) the confidence level
D) 1 − level of significance

Question 37

If a hypothesis test leads to the rejection of the null hypothesis, a _____.

A) Type II error must have been committed
B) Type II error may have been committed
C) Type I error must have been committed
D) Type I error may have been committed

Question 38

In hypothesis testing, the critical value is _____.

A) a number that establishes the boundary of the rejection region
B) the probability of a Type I error
C) the probability of a Type II error
D) the same as the p-value

Question 39

A two-tailed test is a hypothesis test in which the rejection region is _____.

A) in both tails of the sampling distribution
B) in one tail of the sampling distribution
C) only in the lower tail of the sampling distribution
D) only in the upper tail of the sampling distribution

Question 40

A one-tailed test is a hypothesis test in which rejection region is _____.

A) in both tails of the sampling distribution
B) in one tail of the sampling distribution
C) only in the lower tail of the sampling distribution
D) only in the upper tail of the sampling distribution

Question 41

When the p-value is used for hypothesis testing, the null hypothesis is rejected if _____.

A) p-value ≤ α
B) α < p-value
C) p-value > α
D) p-value = z

Question 42

If a hypothesis is rejected at a 5% level of significance, it _____.

A) will always be rejected at the 1% level
B) will always be accepted at the 1% level
C) will never be tested at the 1% level
D) may be rejected or not rejected at the 1% level

Question 43

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually INCREASED the proportion of tourists visiting Rock City. The correct set of hypotheses is _____.

A) H₀: p > .75 Ha: p ≤ .75
B) H₀: p < .75 Ha: p ≥ .75
C) H₀: p ≥ .75 Ha: p < .75
D) H₀: p ≤ .75 Ha: p > .75

Question 44

A two-tailed test is performed at a 5% level of significance. The p-value is determined to be .09. The null hypothesis _____.

A) must be rejected
B) should not be rejected
C) may or may not be rejected, depending on the sample size
D) has been designed incorrectly

Question 45

For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the confidence interval _____.

A) is symmetric
B) is non-symmetric
C) includes µ₀
D) does not include µ₀

Question 46

Which of the following does NOT need to be known in order to compute the p-value?

A) knowledge of whether the test is one-tailed or two-tailed
B) the value of the test statistic
C) the level of significance
D) All of the answers are correct.

Question 47

Excel's __________ function can be used to calculate a p-value for a hypothesis test when σ is unknown.

A) RAND
B) T.DIST
C) NORM.S.DIST
D) Not enough information is given to answer this question.

Question 48

When using Excel to calculate a p-value for an upper-tail hypothesis test, which of the following must be used?

A) RAND
B) 1 − NORM.S.DIST
C) NORM.S.DIST
D) Not enough information is given to answer this question.

Question 49

Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t = _____.

A) 1.328
B) 2.539
C) 1.325
D) 2.528

Question 50

If a hypothesis is not rejected at a 5% level of significance, it will _____.

A) also not be rejected at the 1% level
B) always be rejected at the 1% level
C) sometimes be rejected at the 1% level
D) Not enough information is given to answer this question.

Question 51

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test _____.

A) will result in the rejection region being smaller
B) will result in the rejection region being larger
C) would have no effect on the rejection region
D) Not enough information is given to answer this question.

Question 52

In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is _____.

A) less than or equal to $\alpha$
B) less than or equal to 2 $\alpha$
C) greater than or equal to $\alpha$
D) greater than or equal to 2 $\alpha$

Question 53

Which Excel function would NOT be appropriate to use when conducting a hypothesis test for a population proportion?

A) NORM.S.DIST
B) COUNTIF
C) STDEV
D) All of the answers are correct.

Question 54

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t = _____.

A) 1.383
B) -1.372
C) -1.383
D) -2.821

Question 55

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is _____.

A) H0: p > .35 H_a: p ≥ .35
B) H0: p ≤ .35 H_a: p > .35
C) H0: p ≥ .35 H_a: p < .35
D) H0: p > .35 H_a: p ≤ .35

Question 56

Excel's __________ function can be used to calculate a p-value for a hypothesis test.

A) RAND
B) NORM.S.DIST
C) NORM.S.INV
D) Not enough information is given to answer this question.

Question 57

The school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is _____.

A) H₀: p < .30 Ha: p ≥ .30
B) H₀: p ≤ .30 Ha: p > .30
C) H₀: p ≥ .30 Ha: p < .30
D) H₀: p > .30 Ha: p ≤ .30

Question 58

A p-value is the _____.

A) probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed
B) value of the test statistic
C) probability of a Type II error
D) probability corresponding to the critical value(s) in a hypothesis test

Question 59

When using Excel to calculate a p-value for a lower-tail hypothesis test, which of the following must be used?

A) RAND
B) 1 − NORM.S.DIST
C) NORM.S.DIST
D) Not enough information is given to answer this question.

Question 60

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance; t = _____.

A) 2.12
B) 1.734
C) -1.740
D) 1.740

Question 61

For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value is _____.

A) .0101
B) .0202
C) .0404
D) .4899

Question 62

A national poll reported that 58% of those with Internet access have made purchases online. To investigate whether this percentage applies to its own state, a legislator commissions a study. A random sample of 400 state residents who have Internet access is taken. Of those 400 respondents, 215 said that they have made purchases online. Does this sample provide sufficient evidence to conclude that the state differs from the nation with respect to making purchases online? Use the p-value to conduct the hypothesis test and use a .05 level of significance.

Question 63

From a population of cans of coffee marked "12 ounces," a sample of 25 cans is selected and the contents of each can are weighed. The sample revealed a mean of 11.8 ounces and a standard deviation of 0.5 ounces. Test to see if the mean of the population is at least 12 ounces. (Assume the population is normally distributed.) Use a .05 level of significance.

Question 64

A manufacturer claims that at least 40% of its customers use coupons. A study of 25 customers is undertaken to test that claim. The results of the study follow: At a .05 level of significance, use Excel to test the manufacturer's claim.

Question 65

In a television commercial, the manufacturer of a toothpaste claims that at least four out of five dentists recommend its product. A consumer-protection group wants to test that claim. Identify the hypotheses.

Question 66

At a certain manufacturing plant, a machine produces ball bearings that should have a diameter of 0.500 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 36 ball bearings to test to see if the process is "out of control" (i.e. to test to see if the average diameter differs from 0.500 mm). Assume that the process is maintaining the desired standard deviation of 0.06 mm. The results from the latest sample follow: At a .01 level of significance, use Excel to test whether the process is out of control.

Question 67

The smaller the p-value, the _____.

A) greater the evidence against H₀
B) greater the chance of committing a Type II error
C) greater the chance of committing a Type I error
D) less likely one will reject H₀

Question 68

A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 cm. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 cm. The population standard deviation is 0.44 cm. Determine whether or not the lathe is in perfect adjustment. Use a .05 level of significance.

Question 69

A group of young businesswomen wish to open a high fashion boutique in a vacant store, but only if the average income of households in the area is more than $45,000. A random sample of nine households showed the following results. Use the statistical techniques in Excel to advise the group on whether or not they should locate the boutique in this store. Use a .05 level of significance. (Assume the population is normally distributed.)

Question 70

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a .05 level of significance and determine whether or not the average room price is significantly different from $108.50.

Question 71

If a hypothesis test has a Type I error probability of .05, that means if the null hypothesis is _____.

A) false, it will not be rejected 5% of the time
B) false, it will be rejected 5% of the time
C) true, it will not be rejected 5% of the time
D) true, it will be rejected 5% of the time

Question 72

The rejection region for a one-tailed hypothesis test _____.

A) has an area of 1 - ß
B) has an area equal to the confidence coefficient
C) is in the tail that supports the null hypothesis
D) is in the tail that supports the alternative hypothesis

Question 73

A soft drink filling machine, when in perfect adjustment, fills bottles with 12 ounces of soft drink. A random sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounce. With a .05 level of significance, test to see if the machine is in perfect adjustment. Assume the distribution of the population is normal.

Question 74

The sponsors of televisions shows targeted at the market of 5- to 8-year olds want to test the hypothesis that children watch television AT MOST 20 hours per week. The population of viewing hours per week is known to be normally distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this age group. The resulting data follow: At a .10 level of significance, use Excel to test the sponsors' hypothesis.

Question 75

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the sample information reported below, carry out a test of this statement. Use a .05 level of significance.

Question 76

You are given the following information obtained from a random sample of five observations.
20
18
17
22
18
At a 10% level of significance, use Excel to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.)

Question 77

Several years ago the proportion of Americans aged 18-24 who invested in the stock market was 0.20. A random sample of 25 Americans in this age group was recently taken. They were asked whether or not they invested in the stock market. The results follow: At a .05 level of significance, use Excel to determine whether or not the proportion of Americans 18-24 years old that invest in the stock market has changed.

Question 78

At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The population standard deviation is known to be 3.5 years. Determine whether or not the average age of the evening students is significantly different from 21. Use a .1 level of significance.

Question 79

A sample of 81 account balances of a credit company showed an average balance of $1,200. The population standard deviation is $126. You want to determine if the mean of all account balances is significantly different from $1,150. Use a .05 level of significance.

Question 80

For each shipment of parts a manufacturer wants to accept only those shipments with at most 10% defective parts. A large shipment has just arrived. A quality control manager randomly selects 50 of the parts from the shipment and finds that 6 parts are defective. Is this sufficient evidence to reject the entire shipment? Use a .05 level of significance to conduct the appropriate hypothesis test.