Question

4. Short answer questions. Unless stated otherwise, each part is unrelated In the linear regression model, it was found that the 90% confidence interval for the regression coefficient ? is (1.5, 9.3). What can you say, if anything, about the p-value of test of hypotheses Ho: ß-0 vs.Ha, B 0? a. b. A two-sample t test is performed with Ha: ?1 > ?2 and a test statistic of t =-1.24 is observed. Draw a sketch of the area corresponding to the p-value, and find the range of the p-value when df 12. A teacher finds that the scores of a particularly difficult test were normally distributed with a mean of 76 and standard deviation of 14. If a score of below 60 represents a grade of F (failure), what percent of students failed the test? How many points must be added to the students' scores so that only 5% fail? c. To study the muscle mass decrease with age in women, a nutritionist randomly selected 15 women from each 10-year age group, beginning with age 40 and ending with age 79. The scatter plot of muscle mass versus age is shown below. Please raise any concern that you have for fitting a simple linear regression model. d.

Answer 1

4.

a. Since the 90 % confidence interval (1.5 , 9.3 ) does not contain 0.,we would expect that the regression coefficient is not equal to zero. Therefore, we tend to reject Ho and Ho is rejected when P-value is less than level of significance (alpha). In this case Alpha = 1-0.90 = 0.10

Hence, we would expect a p-value < alpha (since this is a two tailed test )

So, P-value < 0.10

b.

c.

d.

The main concern in fitting a simple linear regression model is that the plotted points should be clustered around the regression line so that the regression line is line of best fit.

Here, we can see that the points are clustered close to the regression line , hence , we can easily fit a simple linear regression model in this case.