Television A researcher wanted to determine the mean number of...

Question

Television 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.

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?

Accepted Answer

A health researcher wants to estimate the average daily sodium intake in milligrams among adults in a region. Previous studies report the population standard deviation as sigma equals 150 mg. What is the minimum sample size required to estimate the true mean within plus or minus 50 mg of 95% confidence? Additionally, explain briefly why increasing the confidence level from 95% to 99% increases the required sample size, assuming the same margin of error and sigma. We have 4 possible answers. N equals 43, N equals 58, N equals 39, and N equals 35, and different reasons for why the sample size increases. Now, we first have our equation for sample size, which uses a modified error equation. This is given by A critical Z multiplied by ser deviation divided by the error, all squared. Now a critical Z is given with alpha divided by 2, which is 0.05 divided by 2, or Z of 0.025. We can find this from a table, but this value is 1.96. We have N equals 1.96. Multiplied by standard deviation. Which in our case, is given to us as 150. Divided by our error of 50, all squared. We cannot simplify this to get approximately 34.6 or N equals 35 when rounded up. So we now have our sample size of N equals 35. Now, the reason why this increases the sample size is because when we go from 95% to 99%, we increase the Z value, which increases the margin of error. This requires a larger sample size to maintain the same margin of error. So, our answer is answer D and equals 35 because of the higher Z value for 99% confidence level. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

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