Section 9.4 Hypothesis Tests for Proportions 455 Step 5. Select the form of the alternate hypothesis. For Example 9.20, we use greater than (Figure G). Step 6. Click OK (Figure H). Figure G Figure H SECTION 9.4 Exercises Exercises 1– 4 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 5 and 6, fill in each blank with the appropriate word or phrase. 5. To test H0 : p = p0 with the methods in this section, the values np0 and n(1 − p0) must both be at least . 10 6. To test H0 : p = p0 with the methods in this section, the population size must be at least times as large as the sample size. 20 In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 7. When testing a hypothesis for a proportion, we assume that the items in the population are divided into two categories. True 8. When testing a hypothesis for a proportion, the alternate hypothesis is always two-tailed. False Practicing the Skills 9. In a simple random sample of size 80, there were 54 individuals in the category of interest. a. Compute the sample proportion ̂p. 0.675 b. Are the assumptions for a hypothesis test satisfied? Explain. Yes c. It is desired to test H0 : p = 0.8 versus H1: p < 0.8. Compute the test statistic z. −2.80 d. Do you reject H0 at the 0.05 level? Yes 10. In a simple random sample of size 60, there were 38 individuals in the category of interest. a. Compute the sample proportion ̂p. 0.633 b. Are the assumptions for a hypothesis test satisfied? Explain. Yes c. It is desired to test H0 : p = 0.7 versus H1: p ≠ 0.7. Compute the test statistic z. −1.13 d. Do you reject H0 at the 0.05 level? No 11. In a simple random sample of size 75, there were 42 individuals in the category of interest. a. Compute the sample proportion ̂p. 0.560 b. Are the assumptions for a hypothesis test satisfied? Explain. Yes c. It is desired to test H0 : p = 0.6 versus H1: p ≠ 0.6. Compute the test statistic z. −0.71 d. Do you reject H0 at the 0.05 level? No 12. In a simple random sample of size 150, there were 90 individuals in the category of interest. a. Compute the sample proportion ̂p. 0.600 b. Are the assumptions for a hypothesis test satisfied? Explain. Yes c. It is desired to test H0 : p = 0.5 versus H1: p > 0.5. Compute the test statistic z. 2.45 d. Do you reject H0 at the 0.05 level? Yes Working with the Concepts 13. Spam: According to SecureList, 71.8% of all email sent in July 2012 was spam. A system manager at a large corporation believes that the percentage at his company may be 80%. He examines a random sample of 500 emails received at an email server, and finds that 382 of the messages are spam. a. State the appropriate null and alternate hypotheses. H0 : p = 0.8, H1: p ≠ 0.8 b. Compute the test statistic z. −2.01 c. Using �� = 0.05, can you conclude that the percentage of emails that are spam differs from 80%? Yes d. Using �� = 0.01, can you conclude that the percentage of emails that are spam differs from 80%? No 14. Confidence in banks: A poll conducted in 2012 by the General Social Survey asked a random sample of 1325 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults
navidi_monk_elementary_statistics_2e_ch7-9
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