Answer to Question #104178 in Statistics and Probability for Katenda

Question

Question 23

In a random sample of 100 people, 25 are classified as meeting a characteristic of interest i.e.
success. Suppose the proportion of success is known to be 0.3. What is the sample proportion p
and the standard error of the proportion  p?

(1) p = 0.3 and  p = 0.0458
(2) p = 0.3 and  p = 0.0433
(3) p = 0.25 and  p = 0.0433
(4) p = 0.25 and  p = 0.0458
(5) None of the above.

Answer 1

$\hat{P}=\frac{25}{100}=0.25$

$SE=\sqrt{\frac{\hat{P}(1-\hat{P})}{n}}$

$SE=\sqrt{\frac{0.25(1-0.25)}{100}}=0.0433$

Thus, the correct answer is (3).