You are testing the null hypothesis that there is no linear relationship between

Question

You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18, you determine that b1=4.5 and Sb1=1.9

a. What is the value of tSTAT?

b. At the =0.05 level of significance, what are the critical values?

c. Based on your answers to (a) and (b), what statistical decision should you make?

d. Construct a 95% confidence interval estimate of the population slope, 1.

Explanation / Answer

Given n = 18 b1 = 4.5 Sb1 = 1.9 a) t-Stat = b1 / Sb1 = 4.5 / 1.9 = 2.3684 t-Stat = 2.3684 b) = 0.05 From t - tables, we find t-critical for = 0.05 and degrees of freedom = n - 2 = 18 - 2 = 16 This is a two tail test Hence we find t(/2, df) = t(0.025, 16) = 2.1199 t-critical = 2.1199 c) Since t-stat (2.3684) > t-critical(2.1199), we reject the null hypothesis Also the p-value for t-Stat for df = 16 is 0.0308 for a two tailed test Since 0.0308 < (0.05), we reject the null hypothesis Statistical Decision : There is statistically significant evidence to show that there is a linear relationship between X and Y d) 95% confidence interval estimate for slope 1 95% confidence interval implies = 0.05 t-critical = 2.1199 … From (b) Confidence interval is given by b1 ± t-critical * Sb1 Thus confidence interval is 4.5 ± 2.1199 x 1.9 = (4.5 ± 4.02781) 95% Confidence interval estimate of population slope is (0.47219, 8.52781)

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