Question

. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of allowable sampling error is 5% and the estimated population standard deviation is unknown. Q/A6.1. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of allowable sampling error is 5% and the estimated population standard deviation is unknown.

Answer 1

900 sample size

Explanation:

To determine the sample size for a proportion, the margin of error formula is used to determine this:

`E=Z_{(\alpha)/(2) }*\sqrt{\frac{\hat p \hat q}{{n} }`

`n=\hat p \hat q*(\frac{Z_{(\alpha)/(2) }}{E} )^2`

Where p is the proportion, E is the margin of error, n is the sample size, q = 1 - p,
`Z_(\alpha )/(2)` is the z score.

Since the proportion is not known, the sample size needed to guarantee the confidence interval and error is at p = 0.5 and q = 1 - p = 1 - 0.5 = 0.5

E = 5% = 0.05,
`Z_(\alpha )/(2)` = 3. Hence:

`n=0.5*0.5*((3)/(0.05) )^2\\\\n = 900`