Question

How large of a sample is needed to estimate the mean of a normally distributed population of each of the​ following?

a.

ME=88​;

σ=49​;

α=0.10

b.

ME=16;

σ=49​;

α=0.10

c. Compare and comment on your answers to parts​ (a) and​ (b).

a.

n=__

​(Round up to the nearest​ integer.)

b.

n=__

​(Round up to the nearest​ integer.)

c. Choose the correct answer below.

A.

Since the standard deviation and significance level are the same in​ (a) and​ (b), the required sample sizes are equal in​ (a) and​ (b).

B.

Holding all else​ constant, increasing the sampling error decreases the required sample size.

C.

Holding all else​ constant, increasing the sampling error increases the required sample size.

Answer 1

a.

The following information has been provided: a 0.10, E 88, o = 49 The critical value for the significance level a 0.10 is ze 1.64. The following formula is used to compute the minimum sample size required to estimate the population mean u within the required margin of error: 2. 1.64 49 = 0.84 n 88 Therefore, the sample size needed to satisfy the condition n 0.84, and it must be an integer number, we conclude that the minimum required sample size is n = 1

b.

The following information has been provided: a 0.1, E 16, o = 49 = 0.1 is ze 1.64. The following formula is used to The critical value for the significance level a compute the minimum sample size required to estimate the population mean u within the required margin of error: 2 1.64 x 49 = 25.38 E 16 Therefore, the sample size needed to satisfy the condition n number, we conclude that the minimum required sample size is n = 26 25.38, and it must be an integer

c.

Correct option : B. Holding all else​ constant, increasing the sampling error decreases the required sample size.