A random sample of 210 of the applicants for a degree course in Policing Practic

Question

A random sample of 210 of the applicants for a degree course in Policing Practice was selected and 43 of them were women.

a. Construct a 95% confidence interval estimate of the true proportion of women who applied to do this course and write a sentence which interprets the confidence limits.

b. Construct a 99% confidence interval estimate of the true proportion of women who applied to do this course. Include the resulting Excel output in your answer. Highlight the upper and lower limits of the confidence interval and write down whether this interval is narrower or wider than the interval in part a.

Explanation / Answer

(a)

Following is the output of confidence interval for proportion:

So required ocnfidence interval is (0.150,.259). We are 95% confident that true population proprotion will lie in the interval  (0.150,.259).

(b)

So requried 99% confidence interval is (0.133,0.277).

It is wider than part (a).

Confidence interval - proportion 95% confidence level 0.2048 proportion 210 n 1.960 z 0.055 half-width 0.259 upper confidence limit 0.150 lower confidence limit

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