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Exam 20: More About Tests

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Question 1

Essay

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A company is willing to renew its publishing contract with a popular calculus book author only if he can prove that his book can sell to more than 15% of the entire calculus market.The publishing company contacts 3000 calculus professors at random and only 420 professors were interested in the book.Should the company renew the contract? Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

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11ea7dab_396a_78bb_b67a_ed1263c468ac_TB3448_11_TB3448_11 : p = 0.15; 11ea7dab_396a_78bc_b67a_496597d7d156_TB3448_11_TB3448_11 : p > 0.15;z = -1.53,p = 0.937.The P-value is greater than the alpha level of 0.05.At the alpha level of 0.05 there is insignificant evidence that the author can sell to more than 15% of the entire calculus market.

Question 2

Multiple Choice

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A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university conducts a hypothesis test to determine if the retention rate has increased and obtains a P-value of 0.075.What is reasonable to conclude about the new programs using α = 0.05?

A) There is a 7.5% chance of the new programs having no effect on the retention rate.
B) We can say there is a 7.5% chance of seeing the new programs having an effect on the retention rate in the results we observed from natural sampling variation.We conclude the new programs are more effective.
C) There is a 92.5% chance of the new programs having no effect on the retention rate.
D) If the new programs have no effect on the retention rate,then there is only a 7.5% chance of seeing the increase in the retention rate that we observed (or higher) from natural sampling variation.At α = 0.05,we reject the null hypothesis that the new programs have no effect on the retention rate and conclude that the programs have been effective in increasing the retention rate.
E) If the new programs have no effect on the retention rate,then there is only a 7.5% chance of seeing the increase in the retention rate that we observed (or higher) from natural sampling variation.At α = 0.05,we fail to reject the null hypothesis that the new programs have no effect on the retention rate.There is insufficient evidence to conclude that the programs have been effective in increasing the retention rate.

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Question 3

Multiple Choice

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According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese;that is,they had a body mass index (BMI) of 30 more higher.Suppose you believe that the percentage of obese Canadians has decreased since 2004 and wish to test your belief.Identify the Type I error in this context.

A company is willing to renew its publishing contract with a popular calculus book author only if he can prove that his book can sell to more than 15% of the entire calculus market.The publishing company contacts 3000 calculus professors at random and only 420 professors were interested in the book.Should the company renew the contract? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

A company has surveyed a sample of its employees to find out how many might take advantage of a weight loss program.The table below shows the results.Give the 95% confidence interval for the group(s)for which we could use our methods of inference for the proportion of employees who would be willing to participate in the program.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.To test their belief,they plan to take a random sample size of 1000 people.If they plan to perform the test at α = 0.01 and the unemployment rate is currently 6.1%,what is the power of the test?

A Math professor has observed over several years that about 38% of the students who initially major in Math drop out of the program after their freshman year.The department head suggested making the curriculum easier by taking a couple of 300 level courses out of the requirements.With the new curriculum intact,207 began their freshman year as Math majors and only 59 dropped out of the program.Should the college continue with the easier curriculum? State the critical value required to perform an appropriate hypothesis test using α = 0.05.

A new manager,hired at a large warehouse,was told to reduce the 26% employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.The manager decides to test the new program to see if it's better and receives a P-value of 0.06.What is reasonable to conclude about the new strategy using α = 0.05?

Five years ago,a company found that 8% of its employees commuted to work by car.A survey investigates whether the current proportion of employees who commute by car to work is higher than it was five years ago.Identify the Type II error in this context.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.You wish to know if the current unemployment rate differs from that of April 2011.You take a random sample size of 1000 and found unemployment at 6.1%.State the critical value required to perform an appropriate hypothesis test using α = 0.05.

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy to see if it's better.What are the null and alternative hypotheses?

A company has surveyed a sample of its employees to find out how many might take advantage of a weight loss program.The table below shows the results.Give the 95% confidence interval for Building A for the proportion of employees who would be willing to participate in the program.Based on this interval,can we say that the proportion differs from 11%? At which level of significance are you making this decision?

The mayor's disapproval rating was previously 13%.After a political ad campaign for a city's mayor,pollsters check the disapproval ratings.They test the hypothesis that the ads produced no change against the alternative that the ratings are now below 13%,and find a P-value of 0.11.Provide an appropriate conclusion using α = 0.10?

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.State the critical value required to perform an appropriate hypothesis test using α = 0.001.

Have harsher laws decreased the number of drivers under the influence? Observations of Friday and Saturday evening traffic failed to find evidence of a significant change compared with ten years ago.The P-value of the study was P = 0.23.

A city claims that 75% of all low income housing is 1500 sq.ft.The tenants believe the proportion of housing this size is smaller than the claim,and hire an independent firm to test a random sample size of 120 and found 1500 sq.ft.housing at 66%.Test an appropriate hypothesis using α = 0.01 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

The seller of a loaded die claims that it will favour the outcome 6.We don't believe that claim,and roll the die 350 times to test an appropriate hypothesis.Our P-value turns out to be 0.01.Provide an appropriate conclusion using α = 0.05?

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 6.1%.Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose you wish to conduct a test to determine if the current unemployment rate differs from that of April 2011.What are the null and alternative hypotheses?

A Science professor has observed over several years that about 15% of the students who initially major in Science drop out of the program after their freshman year.The department head suggested making the curriculum easier by taking a couple of 300 level courses out of the requirements.With the new curriculum in tact,590 began their freshman year as Science majors and only 52 dropped out of the program.Should the college continue with the easier curriculum? Test an appropriate hypothesis using α = 0.05 and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.