Provide an appropriate response.
-A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a $98 \%$ confidence interval for the proportion of college seniors who are planning to pursue a graduate degree.

A) $( 0.616,0.686 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.616$ and $0.686$.
B) $( 0.620,0.682 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.620$ and $0.682$.
C) $( 0.621,0.680 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.621$ and $0.680$.
D) $( 0.612,0.690 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.612$ and $0.690$.

Question

Provide an appropriate response.
-A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a $98 \%$ confidence interval for the proportion of college seniors who are planning to pursue a graduate degree.

A) $( 0.616,0.686 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.616$ and $0.686$.
B) $( 0.620,0.682 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.620$ and $0.682$.
C) $( 0.621,0.680 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.621$ and $0.680$.
D) $( 0.612,0.690 )$; we are $98 \%$ confident that the proportion of college seniors who are planning to pursue a graduate degree is between $0.612$ and $0.690$.

Quizplus · Accepted Answer

To construct a 98% confidence interval for the proportion of college seniors planning to pursue a graduate degree, we use the formula for a confidence interval for a proportion: $\hat{p} \pm z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p} = \frac{658}{1010}$, $n = 1010$, and $z$ is the z-score corresponding to a 98% confidence level (approximately 2.33). Calculating this gives us the interval $(0.616, 0.686)$. This means we are 98% confident that the true proportion of college seniors planning to pursue a graduate degree falls within this interval.

Provide an Appropriate Response 98%98 \%98% Confidence Interval for the Proportion of College Seniors Who Are

Provide an Appropriate Response $98 \%$ Confidence Interval for the Proportion of College Seniors Who Are