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

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, state the null hypothesis for this study.

Which of the following would be an appropriate null hypothesis?

If a researcher rejects a true null hypothesis, she has made a _______error.

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. -True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 1% level of significance.

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.If she wants to have a level of significance at 0.01 What conclusion can she make?

If a researcher does not reject a true null hypothesis, she has made a _______decision.

SCENARIO 9-4 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower.If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision. -Referring to Scenario 9-4, the appropriate hypotheses are:

If a researcher does not reject a false null hypothesis, she has made a _______error.

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 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

True or False: "What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

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: -True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20 during the morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

SCENARIO 9-5 A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years, versus an alternative that the mean age is greater than 45 years.They take a sample and calculate a p-value of 0.0202. -True or False: Referring to Scenario 9-5, the bank can conclude that the mean age is greater than 45 at a significance level of

True or False: In testing a hypothesis, you should always raise the question concerning the purpose of the study, survey or experiment.