Section 8.3 Confidence Intervals for a Population Proportion 387 EXCEL Constructing a confidence interval for a proportion This procedure requires the MegaStat EXCEL add-in to be loaded. The MegaStat add-in may be downloaded from www.mhhe.com/megastat. Step 1. Click on the MegaStat menu and select Confidence Intervals/Sample Size... Step 2. Click on the Confidence interval – p option and enter the value of x in the p field (note that p automatically changes to x) and the value of n in the n field. For Example 8.14, we use x = 403 and n = 517. Step 3. In the Confidence Level field, enter the confidence level. For Example 8.14, enter 95% (Figure F). Step 4. Click Preview (Figure F). Note: The preceding steps produce the traditional confidence interval. To produce the small-sample interval, enter the value of x + 2 for x and the value of n + 4 for n. Figure F SECTION 8.3 Exercises Exercises 1– 6 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 7 and 8, fill in each blank with the appropriate word or phrase. 7. I√f p̂ is the sample proportion and n is the sample size, then ̂p(1 − ̂p) n is the . standard error 8. To estimate the necessary sample size when no value of ̂p is available, we use ̂p = . 0.5 In Exercises 9 and 10, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 9. If we estimate the necessary sample size and no value for ̂p is available, the estimated sample size will be larger than if a value for ̂p were available. True 10. The margin of error does not depend on the sample size. False Practicing the Skills In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n. 11. x = 146, n = 762, confidence level 95% 0.1916, 0.01426, 0.02794 12. x = 46, n = 97, confidence level 99% 0.4742, 0.0507, 0.1306 13. x = 236, n = 474, confidence level 90% 0.4979, 0.02297, 0.0378 14. x = 29, n = 80, confidence level 92% 0.3625, 0.05375, 0.0941 In Exercises 15–18, use the given data to construct a confidence interval of the requested level. 15. x = 28, n = 64, confidence level 93% (0.325, 0.550) 16. x = 52, n = 71, confidence level 97% (0.618, 0.846) 17. x = 125, n = 317, confidence level 95% (0.341, 0.448) 18. x = 178, n = 531, confidence level 90% (0.302, 0.369) Working with the Concepts 19. Smart phone: Among 238 cell phone owners aged 18–24 surveyed by the Pew Research Center, 102 said their phone was an Android phone. a. Find a point estimate for the proportion of cell phone owners aged 18–24 who have an Android phone. 0.429 b. Construct a 95% confidence interval for the proportion of cell phone owners aged 18–24 who have an Android phone. (0.366, 0.491) c. Assume that an advertisement claimed that 45% of cell phone owners aged 18–24 have an Android phone. Does the confidence interval contradict this claim? No
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