Question

Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage. Round the answer to the next larger whole number.

Answer 1

The sample size is
`n = 600`

Explanation:

From the question we are told that

The margin of error is E = 4% = 0.04

From the question we are told the confidence level is 95% , hence the level of significance is

`\alpha = (100 - 95 ) \%`

=>
`\alpha = 0.05`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Since the sample proportion (point estimate of the population proportion was not give we will assume it to be )

`\^ p = 0.5`

Generally the sample size is mathematically represented as

`n = [\frac{Z_{(\alpha )/(2) }}{E} ]^2 * \^ p (1 - \^ p )`

=>
`n = [(1.96)/(0.04) ]^2 * 0.5 (1 - 0.5 )`

=>
`n = 600`