Question

An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. She wants a 95% confidence interval with a margin of error at most ????=0.025m=0.025 . She has no idea what the true proportion could be. How large a sample should she take? 250 1537 1500 400

Answer 1

Answer: 1537

Step-by-step explanation:

Given : Margin of error : $E=0.025$

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

Critical value : $z_{\alpha/2}=z_{0.025}=1.96$

The formula to calculate the sample size if prior estimate pf population proportion does not exist :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.25(\dfrac{1.96}{0.025})^2\\\\\Rightarrow\ n=1536.64\approx1537$

Hence, she should take a sample with minimum size of 1537 .