Out of 100 students sampled, 70 of them said that they hoped to get married someday. With 99.7% confidence, what is the approximate percentage of the students in the population who hope to get married someday?
A. 51.7% to 88.3%
B. 60.8% to 79.2%
C. 65.4% to 74.6%
D. 56.3% to 83.7%

Question

Out of 100 students sampled, 70 of them said that they hoped to get married someday. With 99.7% confidence, what is the approximate percentage of the students in the population who hope to get married someday?
	A.	51.7% to 88.3%
	B.	60.8% to 79.2%
        C.	65.4% to 74.6%
        D.	56.3% to 83.7%

anonymous · Answer

the sample proportion is $\hat p=70/100=0.7$ and the corresponding sample proportion distribution's standard deviation is $\sigma_{\hat p}=\sqrt{\frac1N\hat p(1-\hat p)}\approx0.0458$. 99.7% confidence intervals cover values up to 3 standard deviations from the mean by the empirical rule, so our interval should be approximately $\hat p\pm3\sigma_{\hat p}\approx0.7\pm0.1375=(0.5625,0.8375)$ i.e. the interval is between $56.3\%$ and $83.7\%$

anonymous · Answer

thank you