People were polled on how many books they read the previous year. Initial survey

Question

People were polled on how many books they read the previous year. Initial survey results indicate that s = 14.5 books. Complete parts (a) through (d) below. (a) How many subjects are needed to estimate the mean number of books read the previous year within four books with 95% confidence? This 95% confidence level requires ___ subjects. (Round up to the nearest subject.) (b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95% confidence? This 95% confidence level requires ___ subjects. (Round up to the nearest subject.) (c) What effect does doubling the required accuracy have on the sample size? A. Doubling the required accuracy halves the sample size. B. Doubling the required accuracy quarters the sample size. C. Doubling the required accuracy doubles the sample size. D. Doubling the required accuracy quadruples the sample size. (d) How many subjects are needed to estimate the mean number of books read the previous year within four books with 99% confidence? This 99% confidence level requires ___ subjects. (Round up to the nearest subject.) Compare this result to part (a) How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable? A. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size. B. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with 3 larger sample size. C. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a smaller sample size. D. Increasing the level of confidence decreases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.

Explanation / Answer

Answers below:

s = 14.5
Z = 1.96 for 95% CI

Z = 2.56 for 99% CI

a.Margin of error = 4

4 = 1.96*14.5/sqrt(n)
n = (1.96*14.5/4)^2
= 50.48 or 51

b.

2 = 1.96*14.5/sqrt(n)
n = (1.96*14.5/2)^2
= 201.92 or 202

c. D)Doubling the required accuracy quadrauples the sample size

d.

4 = 2.56*14.5/sqrt(n)
n = (2.56*14.5/4)^2
= 86.1184 or 86 people

e. B is right interpreation of the above results.
i)If MOE is fixed, then greater confidence can be achieved by increasing sample size.
ii) You would have to increase the sample size to increasing the level of confidence

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