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

The marketing manager for a car manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300.The manager believes from previous information that the proportion is 0.30.Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags.If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis,what conclusion could you draw?

Instruction 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture.She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650.The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. -Referring to Instruction 9-6,suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650.Then if the test is performed with a level of significance of 0.10,the null hypothesis would be rejected.

If you know that the probability of committing a Type II error (β)is 5%,you can tell that the power of the test is

The power of a statistical test is

Instruction 9-4 A drug company is considering marketing a new local anaesthetic.The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anaesthetic;otherwise,it will continue to produce the older drug.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 Instruction 9-4,if the level of significance had been chosen as 0.05,the company would market the new anaesthetic.

Instruction 9-2 A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student. -Referring to Instruction 9-2,what is the "actual confidence coefficient"?

Instruction 9-2 A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses.Suppose in actuality that if someone is studying a business major,she can correctly identify that person as a business student 87% of the time.When a person is studying a science major,the student will incorrectly identify that person as a business student 16% of the time.Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major),she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student. -Referring to Instruction 9-2,what would be a Type II error?

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.If she wants to have a level of significance at 0.01,what rejection region should she use?

Instruction 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 Instruction 9.3,the value of the test statistic is ________.

Instruction 9-1 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park.A biologist wants to know if the mean number of parasites per butterfly is greater than 20.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 butterflies: $n = 46 ;$ Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,if these data were used to perform a two-tailed test,the p-value would be 0.042.

If a researcher accepts a false null hypothesis,she has made a ________ error.

The statement of the null hypothesis always contains an equality.

A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores.The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area own DVD players.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players.The p-value associated with the test statistic in this problem is approximately equal to

Instruction 9-4 A drug company is considering marketing a new local anaesthetic.The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anaesthetic;otherwise,it will continue to produce the older drug.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 Instruction 9-4,the null hypothesis will be rejected with a level of significance of 0.10.

Instruction 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 at a 0.01 level of significance. -Referring to Instruction 9-7,the null hypothesis will be rejected if the test statistics is

You have created a 95% confidence interval for μ with the result (10,15).What decision will you make if you test H₀: μ = 16 versus H₁: μ ≠ 16 at α = 0.10?

Instruction 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 at a 0.01 level of significance. -Referring to Instruction 9-7,the value of β is 0.90.

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 was selected.Suppose you reject the null hypothesis.What conclusion can you draw?

Instruction 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 at a 0.01 level of significance. -Referring to Instruction 9-7,what critical value should the company officials use to determine the rejection region?

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