Deck 9: B: large-Sample Tests of Hypotheses

Question 1

Federal Votes Narrative
A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high.
Refer to Federal Votes Narrative. State the appropriate null and alternative hypotheses to be tested by the Liberal party opponent .

Answer 1

, where p is the true proportion of Canadian voters supporting the Conservative party candidate .

Question 2

A new light bulb is being considered for use in an office It is decided that the new bulb will be used only if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance.

Answer 2

The hypotheses to be tested are . The test statistic is = (505 - 500)/(18/ ) = 1.76. Since -2.33 < z < 2.33, we fail to reject the null hypothesis. We conclude that the true average lifetime of the bulb is not significantly larger than 500 (i.e., do not use this bulb.)

Question 3

Defective Toasters Narrative
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
Refer to Defective Toasters Narrative. Describe the Type II error for this .

Answer 3

A Type II error occurs if the manufacturer does not reject the null hypothesis when, in fact, it is false; that is, if the manufacturer does not conclude the proportion of defective switches is more than 0.05 when, in fact, it is.

Question 4

Catalogue Mail-Orders Narrative
A mail-order catalogue claims that customers will receive their product within four days of ordering. A competitor believes that this claim is an underestimate.
Refer to Catalogue Mail-Orders Narrative. State the appropriate null and alternative hypotheses to be tested by the competitor.

Question 5

Federal Votes Narrative
A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high.
Refer to Federal Votes Narrative. Describe the Type I error for this .

Question 6

A sample of size 150 is to be used to test the hypotheses H₀: $\mu$ = 3.75 kg vs. H_a: $\mu$ $\neq$ 3.75 kg, where, $\mu$ is the average weight of a newborn Canadian baby. Give the appropriate rejection region associated with each of the following significance levels.
a. = 0.01
b. = 0.05
c. = 0.1

Question 7

Defective Toasters Narrative
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
Refer to Defective Toasters Narrative. From the supplier's point of view, which error would be the more serious? Justify your answer.

Question 8

Swimming Average Narrative
Historically, the average time it takes Jessica to swim the 200 m butterfly is 148.4 seconds. Jessica would like to know if her average time has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.

-Refer to Swimming Average Narrative. Compute the power of the test if Jessica's actual mean swimming time is 147.3 seconds. Interpret the results.

Question 9

Refer to Swimming Average Narrative. Perform the appropriate test of hypothesis to determine whether Jessica's average time has changed. Use $\alpha$ = 0.01.

Question 10

Catalogue Mail-Orders Narrative
A mail-order catalogue claims that customers will receive their product within four days of ordering. A competitor believes that this claim is an underestimate.
Refer to Catalogue Mail-Orders Narrative. Describe the Type II error for this .

Question 11

Defective Toasters Narrative
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
Refer to Defective Toasters Narrative. From the manufacturer's point of view, which error would be the more serious? Justify your answer.

Question 12

Catalogue Mail-Orders Narrative
A mail-order catalogue claims that customers will receive their product within four days of ordering. A competitor believes that this claim is an underestimate.
Refer to Catalogue Mail-Orders Narrative. Describe the Type I error for this .

Question 13

Develop the null and appropriate hypotheses that are most appropriate for each of the following situations:
a. A meteorologist claims that the average high temperature for the month of August in Montreal is 27°C. If the residents of Montreal do not believe this to be true, what hypotheses should they test?
b. A car manufacturing plant is acting in accordance with the public's interest in making cars that have fuel consumption of at most 8.2 litres per 100 km. The supervisor will let the cars off the manufacturing floor only if the fuel consumption is less than 8.8 L/100 km. What hypotheses should the plant test?
c. A spokesperson for the Health Department reports that a fish is unsafe for human consumption if the polychlorinated biphenyl (PCB) concentration exceeds 5 ppb. The Carlson family is interested in the mean PCB concentration in a fish from the lake on which they live. What hypotheses should they test?
d. An Internet survey revealed that 50% of Internet users received more than 10 email messages per day. A similar study on the use of email was repeated. The purpose of the study was to see whether use of email has increased.

Question 14

Defective Toasters Narrative
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
Refer to Defective Toasters Narrative. State the appropriate null and alternative hypotheses to be tested by the manufacturer.

Question 15

Defective Toasters Narrative
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
Refer to Defective Toasters Narrative. Describe the Type I error.

Question 16

Federal Votes Narrative
A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high.
Refer to Federal Votes Narrative. Describe the practical consequences for the Liberal party opponent if he makes a Type II error.

Question 17

Federal Votes Narrative
A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high.
Refer to Federal Votes Narrative. Describe the Type II error for this .

Question 18

Transport Quebec repaired hundreds of bridges in 1993. To check the average cost to repair a bridge, a random sample of n = 55 bridges was chosen. The mean and standard deviation for the sample are $25,788 and $1540, respectively. Records from previous years indicate an average bridge repair cost was $25,003. Use the sample data to test that the 1993 mean $\mu$ is greater than $25,003. Use $\alpha$ = 0.05.

Question 19

Federal Votes Narrative
A Conservative party candidate in a federal election believes that 54% of Canadian voters are supporting him. His Liberal party opponentbelieves this estimate is too high.
Refer to Federal Votes Narrative. Describe the practical consequences for the Liberal party opponent if he makes a Type I error.

Question 20

A sample of size 80 is to be used to test the hypotheses H₀: $\mu$ = 29 vs. H_a: $\mu$ > 29, where $\mu$ is the average age of a man when he gets married. What is the appropriate rejection region associated with each of the following significance levels?
a. = 0.01
b. = 0.005
c. = 0.05
d. = 0.1

Question 21

University Housing Costs Narrative
A large university claims that the average cost of housing within 3 kilometres of the campus is $6900 per school year. A high school student is preparing her budget for her freshman year at the university. She is concerned that the university's estimate is too low. Having taken statistics, she decides to perform the following test of hypothesis: , where represents the average cost of housing per year within 3 kilometres of the university.
Refer to University Housing Costs Narrative. Describe the Type I error for this .

Question 22

Average Childcare Costs Narrative
The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.

-Refer to Average Childcare Costs Narrative. Find the p-value for the test in the previous question.

Question 23

Swimming Average Narrative
Historically, the average time it takes Jessica to swim the 200 m butterfly is 148.4 seconds. Jessica would like to know if her average time has changed. She records her time on 50 randomly selected occasions and computes the mean to be 147.8 seconds with a standard deviation of 2.3 seconds.

-Let $\mu$ denote the true average delivery time of a letter from a specific carrier. For a large-sample z-test of H₀: $\mu$ = 3 versus H_a: $\mu$$\neq$ 3, find the p-value associated with each of the given values of the test statistic, and state whether each p-value will lead to a rejection of the null hypothesis when performing a level 0.05 test.
a. 2.16
b. 0.38
c. -2.81
d. 1.07
e. -0.68

Question 24

University Housing Costs Narrative Which error has more serious consequences for the student? Explain.

Question 25

Laptop Battery Charge Time Narrative
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information:

-Refer to Laptop Battery Charge Time Narrative. Perform the appropriate test of hypothesis to determine whether there is a significant difference in average functioning time before recharging between the two models of battery packs. Test using = 0.10.

Question 26

Copper Pipes Narrative
A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 cm. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 cm and the sample standard deviation 0.2 cm. Using a significance level of = 0.05, test the appropriate hypotheses.

-An airline company would like to know if the average number of passengers on a flight in November is less than the average number of passengers on a flight in December. The results of random sampling are printed below. Test the appropriate hypotheses using $\alpha$ = 0.01.
November December

Question 27

Average Childcare Costs Narrative
The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.
Refer to Average Childcare Costs Narrative. Perform the appropriate test of hypothesis for the potential resident using = 0.01.

Question 28

Copper Pipes Narrative
A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 cm. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 cm and the sample standard deviation 0.2 cm. Using a significance level of = 0.05, test the appropriate hypotheses.
Refer to Copper Pipes Narrative. Calculate the p-value and write your conclusion.

Question 29

Average Childcare Costs Narrative
The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.

-Refer to Average Childcare Costs Narrative. What effect, if any, would there be on the conclusion of the test of hypothesis in the first question if you changed to 0.05?

Question 30

Medical School Completion Narrative
A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time, on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical school computed:

-Refer to Medical School Completion Narrative. Perform the appropriate test of hypothesis to determine whether there is a significant difference in time to completion of medical school between women and men. Test using $\alpha$ = 0.05.

Question 31

Average Childcare Costs Narrative
The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.
An Internet server claimed that its users averaged 15 hours per week. To determine whether this was an overstatement, a competitor conducted a survey of 150 customers and found that the average time spent online was 13 hours per week with a standard deviation of 6.5 hours. Do the data provide sufficient evidence to indicate that the average hours of use are less than that claimed by the first Internet server? Test at the 1% level of significance.

Question 32

Average Daily Wages Narrative
The daily wages in a particular industry are normally distributed with a mean of $60 and a standard deviation of $13. Suppose a company in this industry employs 50 workers and pays them $57.5 on the average. Based on this sample mean, can these workers be viewed as a random sample from among all workers in the industry?
Refer to Average Daily Wages Narrative. If you planned to conduct your test using what would be your test conclusions?

Question 33

Laptop Battery Time Narrative
The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for eight hours, on average, before having to be recharged. A random sample of 36 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.9 hours.

-Refer to Laptop Battery Time Narrative. Find the p-value for this test.

Question 34

Copper Pipes Narrative
A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 cm. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 cm and the sample standard deviation 0.2 cm. Using a significance level of = 0.05, test the appropriate hypotheses.
Refer to Copper Pipes Narrative. State the appropriate hypotheses.

Question 35

Average Daily Wages Narrative
The daily wages in a particular industry are normally distributed with a mean of $60 and a standard deviation of $13. Suppose a company in this industry employs 50 workers and pays them $57.5 on the average. Based on this sample mean, can these workers be viewed as a random sample from among all workers in the industry?
Refer to Average Daily Wages Narrative. Find the p-value for the test.

Question 36

Copper Pipes Narrative
A manufacturer of copper pipes must produce pipes with a diameter of precisely 5 cm. The firm's quality inspector wants to test the hypothesis that pipes of the proper size are being produced. Accordingly, a simple random sample of 100 pipes is taken from the production process. The sample mean diameter turns out to be 4.98 cm and the sample standard deviation 0.2 cm. Using a significance level of = 0.05, test the appropriate hypotheses.
Refer to Copper Pipes Narrative. Calculate the value of the test statistic.

Question 37

Average Childcare Costs Narrative
The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.

-Refer to Average Childcare Costs Narrative. Find the power of the test when is actually $685 and = 0.05. Interpret the results.

Question 38

Medical School Completion Narrative
A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time, on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical school computed:

-Refer to Medical School Completion Narrative. Find the p-value associated with the test in the previous question.

Question 39

University Housing Costs Narrative Describe the Type II error for this .

Question 40

Laptop Battery Time Narrative
The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for eight hours, on average, before having to be recharged. A random sample of 36 battery packs was selected and placed on test. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.9 hours.
Refer to Laptop Battery Time Narrative. A competitor claims that the manufacturer's claim is too high. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using = 0.05.

Question 41

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. Calculate the p-value.

Question 42

Red Meat Consumption Narrative
To test the theory that the consumption of red meat in Canada has decreased over the past 10 years, a researcher decides to select hospital nutrition records for 400 subjects surveyed 10 years ago and to compare their average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table.
Refer to Red Meat Consumption Narrative. Find a 99% lower confidence bound for the difference in the average per capita beef consumption for the two groups. Does your confidence bound confirm your conclusions in the previous question? Explain. What additional information does the confidence bound give you?

Question 43

Gas Heat Narrative
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heat with gas.

-Refer to Gas Heat Narrative. Find the p-value for this test.

Question 44

Red Meat Consumption Narrative
To test the theory that the consumption of red meat in Canada has decreased over the past 10 years, a researcher decides to select hospital nutrition records for 400 subjects surveyed 10 years ago and to compare their average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table.
In an attempt to compare the starting salaries for graduates who majored in business and education, random samples of 50 recent graduates in each major were selected and the following information was obtained: Do the data provide sufficient evidence to indicate a difference in average starting salaries for graduates who majored in business and education? Test using

Question 45

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. Construct a 95% confidence interval for the difference in mean amount of life insurance held by professional men and women.

Question 46

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. Determine the critical region using a significance level = 0.05.

Question 47

College Beach Volleyball Narrative
A student government representative at a local university claims that 60% of the undergraduate students favour a move from court volleyball to beach volleyball`. A random sample of 250 undergraduate students was selected and 140 students indicated they favoured a move to beach volleyball.

-Refer to College Beach Volleyball Narrative. Perform the appropriate test of hypothesis to test the representative's claim. Use = 0.05.

Question 48

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. What is your conclusion?

Question 49

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. State the appropriate hypotheses.

Question 50

A random sample of 150 observations was selected from a binomial population, and 87 successes were observed. Do the data provide sufficient evidence to indicate that the population proportion p is greater than 0.5? Use the critical value approach and the p-value approach.

Question 51

Gas Heat Narrative
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heat with gas.
The owner of a marina would like to believe that more than 40% of the sailboat owners use their boats more than 6 times each summer. A random sample of 70 sailboat owners showed 42 used their boats more than 6 times each summer. State and test the appropriate hypotheses using a significance level of 0.005. Is there a reason for the marina owner to believe more than 40% of the sailboat owners use their boats more than 6 times each summer?

Question 52

Gas Heat Narrative
A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heat with gas.

-Refer to Gas Heat Narrative. Perform the appropriate test of hypothesis to determine whether the proportion of homes heated by gas has changed. Test using $\alpha$ = 0.05.

Question 53

College Beach Volleyball Narrative
A student government representative at a local university claims that 60% of the undergraduate students favour a move from court volleyball to beach volleyball`. A random sample of 250 undergraduate students was selected and 140 students indicated they favoured a move to beach volleyball.

-Refer to College Beach Volleyball Narrative. Find the p-value for the test in the previous question.

Question 54

Laptop Battery Charge Time Narrative
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information:
Independent random samples of 35 and 50 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here: Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use the p-value approach and the critical value approach and explain your conclusion.

Question 55

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. Explain how to use the 95% confidence interval for to test the appropriate hypotheses at = 0.05.

Question 56

Red Meat Consumption Narrative
To test the theory that the consumption of red meat in Canada has decreased over the past 10 years, a researcher decides to select hospital nutrition records for 400 subjects surveyed 10 years ago and to compare their average amount of beef consumed per year to amounts consumed by an equal number of subjects interviewed this year. The data are given in the table.
Refer to Red Meat Consumption Narrative. Do the data present sufficient evidence to indicate that per capita beef consumption has decreased in the past 10 years? Test at the 1% level of significance.

Question 57

Refer to Plant Experiments Narrative. What hypothesis should you use to test the geneticist's claim?

Question 58

Laptop Battery Charge Time Narrative
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information:

-Refer to Laptop Battery Charge Time Narrative. Find the p-value for the test in the previous question.

Question 59

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.
Refer to Life Insurance Narrative. Calculate the value of the test statistic.

Question 60

Life Insurance Narrative
An insurance company wants to test the hypothesis that the mean amount of life insurance held by professional men equals that held by professional women. Accordingly, two independent simple random samples are taken from appropriate professional listings of men and women. The sample of 200 men reveals a mean amount of $140,000 with a standard deviation of $26,000. The sample of 400 women shows a mean amount of $128,000 with a standard deviation of $3,000.

-The proportion of defective computers built by Byte Computer Corporation is 0.15. In an attempt to lower the defective rate, the owner ordered some changes made in the assembly process. After the changes were put into effect, a random sample of 42 computers was tested, revealing a total of 4 defective computers. Perform the appropriate test of hypothesis to determine whether the proportion of defective computer has been lowered. Use $\alpha$ = 0.01.

Question 61

Plant Experiments Narrative
A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 80% of the offspring resulting from this cross will have red flowers. To test this claim, 120 seeds from this cross were collected and germinated and 84 plants had red petals.
Refer to Plant Experiments Narrative. Calculate the test statistic and its observed significance level (p-value). Use the p-value to evaluate the statistical significance of the results at the 1% level.

Question 62

Nuclear Weapons Freeze Narrative
A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze.
Refer to Nuclear Weapons Freeze Narrative. Set up the rejection region for this test using = 0.05.

Question 63

Allergy Drug Narrative
In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness.
Refer to Allergy Drug Narrative. Explain how to use this confidence interval to test the hypotheses.

Question 64

Union Contract Narrative
A union composed of several thousand employees is preparing to vote on a new contract. A random sample of 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.
Refer to Union Contract Narrative. State the appropriate null and alternative hypotheses.

Question 65

Union Contract Narrative
A union composed of several thousand employees is preparing to vote on a new contract. A random sample of 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.
Refer to Union Contract Narrative. Compute the p-value for the test.

Question 66

Tennis Magazine Narrative
A marketing manager wants to test the hypothesis that 90% of Tennis magazine's subscribers are homeowners. Accordingly, a simple random sample of 80 is taken from the magazine's list of subscribers. The sample turns out to contain 64 homeowners. Use a significance level of = 0.05.
Refer to Tennis Magazine Narrative. Calculate the p-value and write your conclusion.

Question 67

Allergy Drug Narrative
In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness.
Refer to Allergy Drug Narrative. Compute the p-value of the test.

Question 68

Nuclear Weapons Freeze Narrative
A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze.
Refer to Nuclear Weapons Freeze Narrative. Find the appropriate test statistic.

Question 69

Nuclear Weapons Freeze Narrative
A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze.
Refer to Nuclear Weapons Freeze Narrative. State and interpret your conclusion.

Question 70

Business Graduates Earnings Narrative
A professor claims that 70% of business graduates earn more than $45,000 per year. In a random sample of 300 graduates, 195 earn more than $45,000.
Refer to Business Graduates Earnings Narrative. State the appropriate null and hypotheses.

Question 71

Tennis Magazine Narrative
A marketing manager wants to test the hypothesis that 90% of Tennis magazine's subscribers are homeowners. Accordingly, a simple random sample of 80 is taken from the magazine's list of subscribers. The sample turns out to contain 64 homeowners. Use a significance level of = 0.05.
Refer to Tennis Magazine Narrative. Calculate the value of the test statistic.

Question 72

Business Graduates Earnings Narrative
A professor claims that 70% of business graduates earn more than $45,000 per year. In a random sample of 300 graduates, 195 earn more than $45,000.
Refer to Business Graduates Earnings Narrative. Can we reject the professor's claim at the 5% significance level? Justify your conclusion.

Question 73

Nuclear Weapons Freeze Narrative
A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze.
Refer to Environment Canada Project Narrative. Set up the appropriate null and alternative hypotheses.

Question 74

Allergy Drug Narrative
In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness.
Refer to Allergy Drug Narrative. Construct a 95% confidence interval estimate of the population proportion of the users of this allergy drug who experience drowsiness.

Question 75

Allergy Drug Narrative
In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness.
Refer to Allergy Drug Narrative. State the appropriate null and hypotheses.

Question 76

Allergy Drug Narrative
In clinical studies of an allergy drug, 81 of the 900 subjects experienced drowsiness. A competitor claims that 10% of the users of this drug experience drowsiness.
Refer to Allergy Drug Narrative. Is there enough evidence at the 5% significance level to infer that the competitor is correct? Justify your conclusion.

Question 77

Nuclear Weapons Freeze Narrative
A group in favour of freezing production of nuclear weapons believes that the proportion of individuals in favour of a nuclear freeze is greater for those who have seen the movie "The Day After" (population 1) than those who have not (population 2). In an attempt to verify this belief, random samples of size 500 are obtained from the populations of interest. Among those who had seen "The Day After," 228 were in favour of a freeze. For those who had not seen the movie, 196 favoured a freeze.
Refer to Nuclear Weapons Freeze Narrative. Set up the appropriate null and alternative hypotheses.

Question 78

Business Graduates Earnings Narrative
A professor claims that 70% of business graduates earn more than $45,000 per year. In a random sample of 300 graduates, 195 earn more than $45,000.
Refer to Business Graduates Earnings Narrative. Compute the p-value for the test.

Question 79

Tennis Magazine Narrative
A marketing manager wants to test the hypothesis that 90% of Tennis magazine's subscribers are homeowners. Accordingly, a simple random sample of 80 is taken from the magazine's list of subscribers. The sample turns out to contain 64 homeowners. Use a significance level of = 0.05.
Refer to Tennis Magazine Narrative. State the appropriate hypotheses.

Question 80

Union Contract Narrative
A union composed of several thousand employees is preparing to vote on a new contract. A random sample of 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive more than 60% yes votes.
Refer to Union Contract Narrative. Can we infer at the 5% significance level that the new contract will receive more than 60% yes votes? Justify your conclusion.