Exam 19: More About Tests and Intervals

A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so in a test market so that the effectiveness of the marketing campaign may be evaluated. In this context, committing a Type I error I. Occurs when they conclude that the percentage of customers purchasing the company’s brand has increased when in fact it has not. II. Occurs then they conclude that the percentage of customers purchasing the company’s brand has not increased when in fact it has. III. Would result in the company wasting money on a new marketing campaign that does not increase the percentage of customers buying their brand.

Which of the following would increase the power of a test? I.Increase the sample size II.Decrease the significance level III.Increase alpha

A psychologist claims that more than 2.2% of the population suffers from professional problems due to extreme shyness.Identify the Type II in this context.

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of $16.6$ hours and a standard deviation of $2.22$ hours. The correct value of the test statistic for the appropriate hypothesis test is

In 2014, the average math SAT score for students at one school was 472 . Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed from the 2014 mean of 472 . The hypotheses are: :\mu=472 :\mu472 Explain the result of a Type I error.

In the past, the mean running time for a certain type of flashlight battery has been $8.3$ hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: :\mu=8.3 hours :\mu>8.3 hours Explain the result of a Type I error.

A pharmaceutical company has a drug they think is better at lowering blood pressure than the current medication, but it costs more money for consumers. They conduct a significance test on their clinical study $\left( \mathrm { H } _ { 0 } \right.$ : The new drug works the same as the old drug, $\mathrm { H } _ { \mathrm { A } }$ : The new drug works better than the old drug.) Which statement about errors is correct?

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of $16.6$ hours and a standard deviation of $2.22$ hours. The $P$ -value associated with the resulting test statistic is $0.0009$ . At $\alpha = 0.05$ , which of the following is the correct conclusion? I. We reject the null hypothesis. II. We fail to reject the null hypothesis. III. The firm shouldn't need to institute an incentive program because the evidence indicates that professional employees volunteer an average of more than 15 hours per month in their local community.

An entomologist writes an article in a scientific journal which claims that fewer than $6 \%$ of male fireflies are unable to produce light due to a genetic mutation. Identify the Type I error in this context.

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than $5 \%$ . Identify the Type II error in this context.

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture Finds that only 15% of employees are open to new ideas and approaches toward their work. Consequently, the company conducts a program for employees in order to reinforce the new Corporate philosophy.After the program is completed, employees are surveyed to see if a Greater percentage is now open to innovativeness and change.The correct alternative Hypothesis is

In the past, the mean running time for a certain type of flashlight battery has been $8.4$ hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: :\mu=8.4 hours :\mu>8.4 hours Explain the result of a Type II error.

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture Finds that only 15% of employees are open to new ideas and approaches toward their work. Consequently, the company conducts a program for employees in order to reinforce the new Corporate philosophy.After the program is completed, employees are surveyed to see if a Greater percentage is now open to innovativeness and change.Suppose that based on the Sample results the company rejects the null hypothesis when in fact it is true.Which of the Following statements is correct?

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.Last year the average life expectancy of all policyholders was 77 Years.ABI Insurance wants to determine if their clients now have a longer life expectancy, On average, so they randomly sample some of their recently paid policies.The insurance Company will only change their premium structure if there is evidence that people who buy Their policies are living longer than before.Which of the following statement is true about This hypothesis test?

Marcy's Consignment shop is based in Port Angeles, Washington. It offers both male and female never or slightly used clothing and accessories on a consignment basis. Marcy's recently redesigned their website and wants to show that sales have increased. The sales manager selects 30 sales records at random from the store's online client list and she finds a mean increase in spending of $\$ 3.50$ with a standard deviation of $\$ 7.20$ . The resulting $P$ -value for an $\alpha = 0.05$ is

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample 20 of their recently paid policies. The sample has a mean of $78.6$ years and a standard deviation of $4.48$ years. The $\mathrm { P }$ -value associated with the resulting test statistic is $0.063$ . At $\alpha = 0.05$ , which of the following is the correct conclusion? I. We fail to reject the null hypothesis. II. We reject the null hypothesis. III. There is not significant evidence to indicate an increase in average life expectancy.

In 2014 , the average math SAT score for students at one school was 472 . Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 2014 mean of 472 . The hypotheses are: :\mu=472 :\mu472 Explain the result of a Type II error.