Stat 351 Homework #3 (Section 14.5-14.8) Due date: Tuesday (Oct. 03) at the begi

Question

Stat 351 Homework #3 (Section 14.5-14.8) Due date: Tuesday (Oct. 03) at the beginning of the class. Make sure to show your work if you did any caleulation, and Minitab output if you used Minitab. 1. This problem involves the same data set as Problem 1 in Homework 2 Problem 2 on Page 608 in your textbook). From Homework 2 it is known that the estimated regression equation is 9268-3x. Suppose SST = 1850, SSE = 230, sbi-0.653. Do NOT use Minitab for this problem. a) Carry out a t-test to see whether the predictor is significant. Use = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps. Carry out an F-test to see whether the predictor is significant. Use = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps. b)

Explanation / Answer

a)

test-statstic = (b1^ - b1 under null )/se(b1^)

= (-3 -0) /0.653

= -4.59418

df =n-2 = 5-2 = 3

critical value = 3.187 for alpha = 0.05

since |TS| > critical value

we reject the null hypothesis

b)

SSR = SST - SSE = 1850 -230 = 1620

k = 1 , n = 5

F = (SSR/( k ) )/ (SSE/(n-k-1 )

=   (1620/1)/(230/3)

= 21.13043

critical value =   10.13    {df1 = 1 , df2 = 3 }

since TS> critical value we,reject the null and conclude that the result is significant

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