Number of the elements in the sample is givin n 250 1123 Re

Number of the elements in the sample is givin n = 250.

11-23 Recall the reression of percent body fat on BMI from exercise 11-1

_{a) Estimate the error standard deviation ?}

the answer is:

b) Estimate the standard deviation of the slope?

the answer is:

c) what is the value of the t-statistic for the slope ?

the answer is:

T_{0 = 17.58}

Number of the elements in the sample is givin n = 250. 11-23 Recall the reression of percent body fat on BMI from exercise 11-1 a) Estimate the error standard deviation ? the answer is: alpha = 0.05. What is the P-value for this test ? what is the answer ? beta1 =0 at seeta1 = 0.105 c) what is the value of the t-statistic for the slope ? the answer is: T0 = 17.58 d) Test the hypothesis that sqrt{30.75^{2}} = 5.546 b) Estimate the standard deviation of the slope? the answer is: sqrt{sigma ^{2}}=sigma=

Solution

Answer:

The p value for the test can be found as:

We know that the t statistic is 17.58

Here the number of dregrees of freedom is n-1= 249

On testing the null that H0: B1 =0

against Alternative that H1: B1 ? 0

The t value is 17.58 and the area corresponding to the two tail test is very small, even lesser than 0.0001.

This is found from the t table. The probability of the t statistic exceeding 17.58 is very low, lesser than 0.0001 if the null were true.

The p value being so small i.e. less than 0.05, we can reject the null hypothesis that B1=0.