2. Sample Size You have been hired by your new employer to survey adults about p

Question

2. Sample Size

You have been hired by your new employer to survey adults about printed newspaper subscriptions.

a. If you want to estimate the percentage of adults who have a paid subscription to a printed newspaper, how many adults must you survey if you want 95% confidence that your percentage has a margin of error of three percentage points?

b. If you want to estimate the mean amount that adults have spent on printed newspapers within the past year, how many adults must you survey if you want 95% confidence that your sample mean is in error by no more than $5? (Based on results from a pilot study, assume that the standard deviation of amounts spent on printed newspapers in the last year is $47.)

c. If you plan to obtain the estimates described in parts (a) and (b) with a single survey having several questions, how many adults must be surveyed?

Explanation / Answer

Q.2 (a) margin of error = 3% = 0.03

margin of error = critical test statistic * standard error of proportion

critical test statistic = 1.96

we will take p = 0.05 for minimum sample size n

standard error of proportion = sqrt [ 0.5 * 0.5/n] = 0.5/ sqrt(n)

0.03 = 1.96 * 0.5/ sqrt(n)

sqrt(n) = 32.6667

n = 1067.11 or 1068

(b) Here maximum sample mean error = $5

margin of error = 5 =  critical test statistic * standard error of mean

5 = 1.96 * s/ sqrt(n)

5 = 1.96 * 47/ sqrt(n)

sqrt(n) = 1.96 * 47/5 = 18.424

n = 339.44 = 340

(c) Whichever number is higher among these two, that much adults must be surveyed so we shall surbey 1068 persons withing a single survey.

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