A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches TV. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours. How many people are needed to estimate the number of hours people watch television per week within 1 hour with 95% confidence? Z a/2=1.96
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Step 1
The formula is: n = (Z a/2 * s / E)^2 where: n = sample size Z a/2 = z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence) s = standard deviation of the population (in this case, 7.5 hours) E = desired margin of error (in Show more…
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A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that $s=7.5$ hours. (a) How many people are needed to estimate the number of hours people watch television per week within 2 hours with $95 \%$ confidence? (b) How many people are needed to estimate the number of hours people watch television per week within 1 hour with $95 \%$ confidence? (c) What effect does doubling the required accuracy have on the sample size? (d) How many people are needed to estimate the number of hours people watch television per week within 2 hours with $90 \%$ confidence? Compare this result to part (a). How does decreasing the level of confidence in the estimate affect sample size? Why is this reasonable?
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