The heights were measured for nine supermodels They have a m

The heights were measured for nine supermodels. They have a mean of 65.1 in. and a standard deviation of 1.1 in. Use the traditional method and a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean of 63.6 in. for women from the general population. Click the icon to view a table of critical t-values. Choose the correct answer below. A. Do not reject H0 since the test statistic 0.244 is not greater than the critical value 2.896. B. Reject Ho since the test statistic 0.244 is not greater than the critical value 2.896. C. Reject Ho since the test statistic 4.091 is greater than the critical value 2.896. D. Do not reject Ho since the test statistic 4.091 is greater than the critical value 2.896.

Solution

Given µ = 63.6n= 9 x-bar = 65.1s = 1.1

The null hypothesis is

Against the alternative hypothesis

The test statistic t is given by

t = ((x-bar) - µ)/(s/n-1) t_(n-1)

t = (65.1 -63.6)/(1.1/9-1) t_(9-1)

t = (1.5)/ 0.3889 t₍₈₎

since t_tab =2.896 at 8 degrees of freedom at = 0.01 level of significance

Therefore t_cal> t_tab i.e., we reject the null hypothesis at the given critical value

C) reject H₀ since the test statistic is 3.8570 is greater than the critical value 2.896