Question

Which of the following is the correct conclusion for the hypothesis test? A. Do not reject Ho; the data do not provide sufficient evidence to conclude that x is useful for predicting y. O B. Reject Ho; the data provide sufficient evidence to conclude that x is useful for predicting y. ° C. Reject Ho, the data do not provide sufficient evidence to conclude that x is useful for predicting y. D. Do not reject Ho;the data provide sufficient evidence to conclude that x is useful for predicting y b. Find a 90% confidence interval for the slope of the population regression line. The 90% confidence interval for ß1 is from to (Round to three decimal places as needed.) For the data and sample regression equation shown below, do the following. a. Decide, at the 10% significance level whether the data provide sufficient evidence to conclude b. Find a 90% confidence interval for the slope of the population regression line aks useful or predicting 213 4 8 Σ,-10, Σ 2 = 30, b1-3.3, and se-3.7616 y®-5+3.3x Click here to view the critical t-values page 1. Click here to view the critical t-values page 2. a. What are the hypotheses for the test? D. Ho: P1 and H 1 What is the test statistic? (Round to two decimal places as needed.) Find the P-value. Choose the correct range of values below.

Answer 1

Applying regression on above data:

(x-x) (y-y) 1.3750 7.1250 0.1250 10.8750 16.5000 (x-x) 0.2500 2.2500 0.2500 2.2500 5.0000 (y-y) 7.5625 22.5625 0.0625 52.5625 82.7500 S.No 1 2 2 4. 4 1 10 2.5000 Total 13 3.2500 SSY Mean SSX sample size: here 4 3.2500 2.5000 from above 5.0000 16.5000 slope- 3.30000 intercept- 5.00000 hence line equation: SST Syy- 5.000 3.300 x 82.7500 28.3000 54.4500 SSR (Sxy)/Sxx- error variance σ2- S-SSE/(n-2) 14.150 std error σ 3.7616 null hypothesis Alternate Hypothesis 0 0 for 0.05 level,two tailed test and n-2-2 degree of freedom, critical Decision rule: 4.3027 reject Ho if absolute value of test statistic |t|>4.303 estimated standard error of slope se(P1)- 1.6823 β/se(A) test stat t 1.9616 for 90 % CI value of margin of error E-t*std error lower confidence bound-estimated slope-margin of error Upper confidence bound-estimated slope+margin of error- 2.9200 4.912 -1.612 8.212

a)

option B is correct for hypothesis

test statistic t =1.96

p value =0.1888

for conclusion: option A is correct

b)

90% COnfidence interval =-1.612 , 8.212