Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To Test this claim against the alternative that the actual proportion of doctors who recommend aspirin Is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend Aspirin.The value of the test statistic in this problem is approximately equal to:

True or False: The larger the p-value, the more likely you are to reject the null hypothesis.

SCENARIO 9-2 A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses.Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time.When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time.Presented with one person and asked to identify the major of this person (who is either a business or an agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major. -Referring to Scenario 9-2, what is the value of

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

True or False: For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of The club.She would now like to determine whether or not the mean age of her customers is Greater than 30.If so, she plans to alter the entertainment to appeal to an older crowd.If not, no Entertainment changes will be made.Suppose she found that the sample mean was 30.45 years And the sample standard deviation was 5 years.What is the p-value associated with the test Statistic?

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims That over the past 5 years, the mean daily revenue was $675 with a population standard deviation Of $75.A sample of 30 days reveals a daily mean revenue of $625.If you were to test the null Hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, What can you conclude?

SCENARIO 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 cases: -Referring to Scenario 9-1, what critical value should the manager use to determine the rejection Region?

True or False: "Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test

If an economist wishes to determine whether there is evidence that mean family income in a Community exceeds $50,000

A manager of the credit department for an oil company would like to determine whether the mean Monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100 Accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65.If You were to conduct a test to determine whether the auditor should conclude that there is Evidence that the mean balance is different from $75, which test would you use?

SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. -Referring to Scenario 9-3, for a test with a level of significance of 0.05, the critical value would be ________.

True or False: For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer group has decided to try to discover if the claim appears true.They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. -Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer's claim Appears reasonable are:

A Type II error is committed when

SCENARIO 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant.A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift.She will make her decision using a test with a level of significance of 0.10.The following information was extracted from the Microsoft Excel output for the sample of 46 cases: -Referring to Scenario 9-1, the parameter the manager is interested in is:

Which of the following would be an appropriate alternative hypothesis?