Question

Preliminary estimates suggest that about 58% of students at a state university favor implementing an honor code.

To obtain a 95% confidence interval for the proportion of all students at the university favoring the honor code, what is the minimum sample size needed if the total width of the confidence interval must be less than 5 percentage points (i.e., the confidence interval should extend at most 2.5 percentage points above and below the sample proportion)?
a. 375.
b. 264.
c. 1,498.
d. The answer cannot be determined from the information given.

Answer 1

Answer: c. 1498

Explanation:

Given : Preliminary estimates suggest that about 58% of students at a state university favor implementing an honor code.

i.e. p = 0.58

Significance level :
`\alpha=1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

Margin of error =
`2.5\5=0.025`

The formula to find the sample size is given by :-

`n=p(1-p)((z_(\alpha/2))/(E))^2\\\\=(0.58)(1-0.58)(((1.96))/(0.025))^2\\\\=1497.302016\approx1498`

Hence, the minimum sample size needed = 1498