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Chapter 11: Q. 11.44 (page 460)
Obtain a sample size
Margin of error
Confidence level
Likely range
The required sample size is
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a. Determine the sample proportion.
b. Decide whether using the one-proportion test is appropriate.
c. If appropriate, use the one-proportion test to perform the specified hypothesis test.
In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "... we should be aware that, if the observed value of is closer to than is our educated guess, the margin of error will be larger than desired." Explain why.
One-Proportion Plus-Four z-Interval Procedure. To obtain a plus four -interval for a population proportion, we first add two successes and two failures to our data (hence, the term "plus four") and then apply Procedure on page to the new data. In other words, in place of (which is ), we use . Consequently, for a confidence level of , the endpoints of the plus-four -interval are
As a rule of thumb, the one-proportion plus-four -interval procedure should be used only with confidence levels of or greater and sample sizes of or more.
Christmas Presents. The Arizona Republic conducted a telephone poll of Arizona adults who celebrate Christmas. The question asked was, "In your family, do you open presents on Christmas Eve or Christmas Day?" Of those surveyed, said they wait until Christmas Day.
a. Determine and interpret the sample proportion.
b. At the significance level, do the data provide sufficient evidence to conclude that a majority (more than ) of Arizona families who celebrate Christmas wait until Christmas Day to open their presents?
Is College Worth It? In the New York Times article "College Graduates Fare Well in Jobs Market, Even Through Recession," C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates, 35 were unemployed; and of a random sample of 1008 high-school graduates (no college), 69 were unemployed.
a. At the 1 T significance level, do the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates?
b. Find and interpret a confidence interval for the difference in unemployment rates of college and high-school graduates.
Drinking Habits. In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, American adults were asked, among other things, whether they drink alcoholic beverages at least once a week; said "yes." Determine and interpret a confidence interval for the proportion, , of all American adults who drink alcoholic beverages at least once a week.
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