5. Consider a population having a standard deviation equal to 10. We wish to est

Question

5. Consider a population having a standard deviation equal to 10. We wish to estimate the mean of this population. a) How large a random sample is needed to construct a 95 percent confidence interval for the mean of this population with a margin of error equal to 17 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 295, calculate the 95 percent confidence interval for the population mean. What is the interval's margin of error?

Explanation / Answer

Solution:-

5)

S.D = 10

a) The sample needed to construct a 95% confidence interval for mean of this population with a margin of error equal to 1 is 385.

zalpha/2 = 1.96

S.D = 10

M.E = 1

M.E = zalpha /2 × (S.D)/(sqrt{n})

n = ({zalpha /2 × S.D}/(M.E) )^{2}

n = 384.16

n = 385

b) 95% confidence interval for the population mean is C.I = (294, 296).

C.I = xbar + zalpha /2 × S.E

C.I = 295 + 1.96 × 0.50965

C.I = 295 + 1

C.I = (294, 296)

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