Question

Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal means that the paper will live forever in libraries. The British Medical Journal combines the two: it prints short and readable versions, with longer versions available online. Is this OK with authors? The journal asked a random sample of 96 of its recent authors several questions. One question was "Should the journal continue using this system?" In the sample, 75 said "Yes". Recall, critical values of Z* are found in Table C, except for the one at the 97% confidence level which has a Z*=2.170.

Solving the problem step by step, find the following values (±0.0001).

The sample proportion of authors answering "Yes": p^ = __

The standard error of p^ : __

For a 95 % confidence level for the proportion of all authors that would say "Yes" if asked,

the margin of error is __ , and the confidence interval is __⩽p⩽.__

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 75 / 96 = 0.7813

1 - = 1 - 0.7813 = 0.2187

Z/2 = Z0.015 = 2.170

=  [p( 1 - p ) / n] = [(0.7813 * 0.2187) / 96 ] = 0.0422

Margin of error = E = Z / 2 *

= 2.170 * 0.0422

= 0.0916

A 97% confidence interval for population proportion p is ,

- E < p < + E

0.7813 - 0.0916 < p < 0.7813 + 0.0916

( 0.6897 < p < 0.8729 )