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 = 18.2 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. b) How many subjects are needed to estimate the mean number of books read the previous year within two books with 95% confidence level 95% confidence level requires subjects. (c) What effect does doubting 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. Compare this result to pan (a). How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable? A. 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. 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.

Explanation / Answer

s= 18.2 books

(a) As the width of 95% confidence interval is less than 4 books

so 4 = 2 * Z95% (s/n)

Z95% = 1.96

2 = 1.96 (18.2/n)

n = 1.96 * 18.2/2 = 17.836

n = 318.22 so n = 319

(b)

As the width of 95% confidence interval is less than 2 books

so 2 = 2 * Z95% (s/n)

Z95% = 1.96

1 = 1.96 (18.2/n)

n = 1.96 * 18.2 = 35.672

n = 1272.50 = 1273

(c) doubling the required accuracy will prompts an increase of four fold in sample size.

(d)

As the width of 99% confidence interval is less than 4 books

so 4 = 2 * Z99% (s/n)

Z99% = 2.575

2 = 2.575 (18.2/n)

n = 2.575 * 18.2/2 = 23.4325

n = 549.08 so n =550

Option B is correct. Incresing the level of confidence increases the sample size required. For a fixed marign of error, greater confidencegreater confidence can be achieved with a smaller sample size.

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