Question

3. It is believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 6% with 90% confidence?

Answer 1

Answer: 141

Explanation:

Let p be the population proportion of adults over 50 never graduated from high school.

As per given , we have

Prior estimate of proportion for adults with 5 to 30 age graduated from high school group : p= 0.25

Significance level :
`\alpha: 1-0.90=0.10`

Critical z-value :
`z_(\alpha/2)=1.645`

Margin of error : E= 0.06

Sample size will be :-

`n=p(1-p)((z_(\alpha/2))/(E))^2\\\\=0.25(1-0.25)((1.645)/(0.06))^2`

Simplify ,

`n=140.938802083\approx141`

Hence, the required sample size younger age group be surveyed = 141