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

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the probability of a Type I error is _____ if the population mean bulb life is 510 hours.

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 value of the test statistic is ________.

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this has proven that the null hypothesis is true.

SCENARIO 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company's history.A series of new television advertisements featuring well-known entertainers and sports figures were launched.A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot".A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%.Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e.if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22)at a 0.01 level of significance. -Referring to Scenario 9-7, what will be the p-value if these data were used to perform a two-tail test?

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, which test would you use?

If the Type I error for a given test is to be decreased, then for a fixed sample size

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, the lowest level of significance at which the null hypothesis can still be rejected is ______.

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 "actual confidence coefficient"?

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. -Referring to Scenario 9-5, the null hypothesis would be rejected at a significance level of = 0.01.

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 II error will increase.

In checking normality assumptions for using the t test when σ is not known, which of the following is not true?

Suppose you want to test versus Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?

Which of the following is true regarding setting up a hypothesis test?

The symbol for the power of a statistical test is

Suppose, in testing a hypothesis about a mean, the Z test statistic is computed to be 2.04.The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.

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 a 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, if the level of significance had been chosen as 0.05, the null hypothesis would be rejected.

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 ?

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.The appropriate hypotheses to test are:

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, the population the president is interested in is:

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: n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: T Test Statistic = 2.09; One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject. -Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.