Question

A copyeditor thinks the standard deviation for the number of pages in a romance novel is six. A sample of 25 novels has a standard deviation of nine pages. At , is this higher than the editor hypothesized?

Answer 1

Answer:

No, the standard deviation for number of pages in a romance novel is six only.

Step-by-step explanation:

First we state our Null Hypothesis, $H_o$ : $\sigma$ = 6

             and Alternate Hypothesis, $H_1$ : $\sigma$ > 6

We have taken these hypothesis because we have to check whether our population standard deviation is higher than what editor hypothesized of 6 pages in a romance novel.

Now given sample standard deviation, s = 9 and sample size, n = 25

To test this we use Test Statistics = $\frac{(n-1)s^{2} }{\sigma^{2} }$ follows chi-square with (n-1) degree of freedom [$\chi ^{2}_n__-1$]

       Test Statistics = $\frac{(25-1)9^{2} }{6^{2} }$ follows $\chi ^{2}_2_4$  = 54

and since the level of significance is not stated in question so we assume it to be 5%.

Now Using chi-square table we observe at 5% level of significance the $\chi ^{2}_2_4$ will give value of 36.42 which means if our test statistics will fall below 36.42 we will reject null hypothesis.

Since our Test statistics is more than the critical value i.e.(54>36.42) so we have sufficient evidence to accept null hypothesis and conclude that our population standard deviation is not more than 6 pages which the editor hypothesized.