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

TABLE 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 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 Table 9-2, what would be a Type I error?

If we are performing a two-tailed test of whether µ = 100, the probability of detecting a shift of the mean to 105 will be ____the probability of detecting a shift of the mean to 110.

For a given sample size n, if the level of significance (α) is decreased, the power of the test

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000

TABLE 9- 1 Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 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 Monarch butterflies: n=46; Arithmetic Mean =28.00; Standard Deviation =25.92; Standard Error =3.82; Null Hypothesis: :\mu\leq20.000;\alpha=0.10;df=45;T Test Statistic =2.09; One-Tailed Test Upper Critical Value =1.3006; p-value =0.021; Decision = Reject. -Referring to Table 9-1, the null hypothesis would be rejected if a 4% probability of committing a Type I error is allowed.

The symbol for the power of a statistical test is

TABLE 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's web site was 10.1% The web site at the company was redesigned in an attempt to increase its conversion rates. Samples of 200 browsers at the redesigned site were selected. Suppose that 24 browsers made a purchase. The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Table 9-8, the null hypothesis will be rejected if the test statistics is

TABLE 9-1 Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 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 Monarch butterflies: n=46; Arithmetic Mean =28.00; Standard Deviation =25.92; Standard Error =3.82; Null Hypothesis: :\mu\leq20.000;\alpha=0.10;df=45;T Test Statistic =2.09; One-Tailed Test Upper Critical Value =1.3006; p-value =0.021; Decision = Reject. -Referring to Table 9-4, the p-value of the test is _____.

The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

Suppose we want to test H₀ : µ ? 30 versus H₁ : µ < 30. 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?

TABLE 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 Table 9-6, if the test is performed with a level of significance of 0.10, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

TABLE 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a 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 an average of 257.3 W. -Referring to Table 9-3, what is the power of the test if the average power consumption of all such microwave ovens is in fact 248 W using a 0.10 level of significance?

TABLE 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 Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. Then if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

TABLE 9- 1 Microsoft Excel was used on a set of data n=46; Arithmetic Mean =28.00; Standard Deviation =25.92; Standard Error =3.82; Null Hypothesis: :\mu\leq20.000;\alpha=0.10;df=45;T Test Statistic =2.09; One-Tailed Test Upper Critical Value =1.3006; p-value =0.021; Decision = Reject. -Referring to Table 9-1, the probability of committing a Type II error is _ if the mean number of parasites per butterfly on Monarch butterflies in Pismo Beach State Park is 24 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

TABLE 9- 1 Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 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 Monarch butterflies: =46; Arithmetic Mean =28.00; Standard Deviation =25.92; Standard Error =3.82; Null Hypothesis: :\mu\leq20.000;\alpha=0.10;df=45; T Test Statistic =2.09; One-Tailed Test Upper Critical Value =1.3006; p-value =0.021; Decision = Reject -Referring to Table 9-1, what critical value should the biologist use to determine the rejection region?

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.

Which of the following would be an appropriate null hypothesis?

TABLE 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 average 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 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 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 Table 9-4, if the level of significance had been chosen as 0.05, the company would market the new anesthetic.

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 over 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 be 99% confident in her decision, what rejection region should she use?

TABLE 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 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 Table 9-2, what is the value of ??