Question

Annual revenues are used to predict the value of a baseball franchise. A sample of 32 franchises was used. An analysis of variance of these data showed that b1= 5.0785 and Sb1 = 0.2357.

a. At the 0.05 level of​ significance, is there evidence of a linear relationship between annual revenue and franchise​ value?

b. Construct a​ 95% confidence interval estimate of the population​ slope, β1.

a: Compute the test statistic. tSTAT= ​(Round to four decimal places as​ needed.)

The critical​ value(s) is(are) ​(Round to four decimal places as​ needed.)

b: The​ 95% confidence interval is ____ ≤ β1 ≤ ____ ​(Round to four decimal places as​ needed.)

Answer 1

Solution:

Given:

Sample size = n = 32

b₁= 5.0785 and S_b1 = 0.2357

Part a. At the 0.05 level of​ significance, is there evidence of a linear relationship between annual revenue and franchise​value?

Compute the test statistic. t_STAT=........?

The critical​ values are:

df = n - 2 = 32 - 2 = 30

level of​ significance = 0.05

use Excel command:

=T.INV.2T( probability , df)

=T.INV.2T(0.05,30)

=2.0423

Thus t critical values are: ( -2.0423 , 2.0423)

Since t test statistic value = 21.5465 > 2.0423, we reject null hypothesis that there is no  linear relationship between annual revenue and franchise​value.

Thus there is sufficient evidence of a linear relationship between annual revenue and franchise​value.

Part b. Construct a​ 95% confidence interval estimate of the population​ slope, β1

Formula:

where

Thus

The​ 95% confidence interval is 4.5971 ≤ β1 ≤ 5.5599