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

Question

16. People were polled on how many books they read the previous year. Initial survey results indicate that s= 16.8 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? O A. Doubling the required accuracy nearly halves the sample size. O B. Doubling the required accuracy nearly quarters the sample size. O C. Doubling the required accuracy nearly quadruples the sample size. O D. Doubling the required accuracy nearly doubles 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? O A. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size. O B. 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. O C. 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. O D. 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.

Explanation / Answer

PART A.

Compute Sample Size  

n = (Z a/2 * S.D / ME ) ^2

Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )

Standard Deviation ( S.D) = 16.8

ME =4

n = ( 1.96*16.8/4) ^2

= (32.93/4 ) ^2

= 67.77 ~ 68

PART B.

Compute Sample Size  

n = (Z a/2 * S.D / ME ) ^2

Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )

Standard Deviation ( S.D) = 16.8

ME =2

n = ( 1.96*16.8/2) ^2

= (32.93/2 ) ^2

= 271.06 ~ 272

PART C.

Doubling the require accuracy nearly quarters the sample size

PART D.

Compute Sample Size  

n = (Z a/2 * S.D / ME ) ^2

Z/2 at 0.01% LOS is = 2.576 ( From Standard Normal Table )

Standard Deviation ( S.D) = 16.8

ME =4

n = ( 2.576*16.8/4) ^2

= (43.28/4 ) ^2

= 117.06 ~ 118

PART E.

Increasing the level of confidence increases the sample size required. For a fixed margin of

error, greater confidence can be achieved wh a larger sample size.

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