Question

It is believed that as many as 23% 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. Question 1. How many of this younger age group must we survey in order to estimate the proportion of non-grads to within .10 with 90% confidence

Answer 1

Answer: here are 48 adults of this younger age group.

Step-by-step explanation:

Since we have given that

Error = 0.10

p = 23% = 0.23

At 90% level of significance, i.e. α = 0.10

So, the value of z = 1.645

$n=(\dfrac{z}{E})^2p(1-p)\\\\n=(\dfrac{1.645}{0.1})^2(0.23)(1-0.23)\\\\n=270.6025\times 0.23\times 0.77\\\\n=47.92\\\\n\approx 48$

Hence, there are 48 adults of this younger age group.