Question

Consider a population having a standard deviation equal to 9.94. We wish to estimate the mean of this population.

(a) How large a random sample is needed to construct a 95% confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.)

The random sample is             units.

(b) Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 256, calculate the 95% confidence interval for the population mean. What is the interval’s margin of error? (Round your answers to the nearest whole number.)

The 95% confidence interval is            [, ] .

Margin of error            

Answer 1

a)

Sample size = (Z * / E)²

= ( 1.96 * 9.94 / 1)²

= 379.56

Sample size = 380 (Rounded up to nearest integer)

b)

Margin of error = Z * / sqrt(n)

= 1.96 * 9.94 / sqrt(380)

= 1

95% confidence interval is

- E < < + E

256 - 1 < < 256 + 1

255 < < 257

The 95% CI is ( 255 , 257)