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

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,for a test with a level of significance of 0.10,the critical value would be ________.

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 value of the test statistic in this problem is approximately equal to

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?

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 would be rejected.

The larger is the p-value,the more likely one is to reject the null hypothesis.

Which of the following would be an appropriate alternative hypothesis?

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 population of interest 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,state the alternative hypothesis for this study.

Referring to Instruction 9-1,what critical value should the biologist use to determine the rejection region?

The symbol for the probability of committing a Type II error of a statistical test is

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.

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.State the test of hypothesis that is of interest to the rental chain.

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

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,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 30 using a 0.05 level of significance and assuming that the population standard deviation is 25.92.

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 p-value of the test is ________.

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is 0.05.

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 null hypothesis will be rejected at 5% level of significance.

For an experiment,the probability of a Type I error is 0.05 and the probability of a Type II error is 0.20.The power of the test is

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,for a test with a level of significance of 0.05,the critical value would be ________.

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,what is the probability of making a Type II error if the mean effective time of the anaesthetic is 7.0 using a 0.05 level of significance?