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 $b_1 = 4.5$ and $S_{b_1} = 1.6$. a. What is the value of $t_{STAT}$? b. At the $alpha = 0.05$ 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, $eta_1$. a. What are the hypotheses to test? A. $H_0: eta_1 = 0$ $H_1: eta_1 eq 0$ B. $H_0: eta_1 ge 0$ $H_1: eta_1 < 0$ C. $H_0: eta_1 eq 0$ $H_1: eta_1 = 0$ D. $H_0: eta_1 le 0$ $H_1: eta_1 > 0$ $t_{STAT} = 2.81$ (Round to two decimal places as needed.) b. The lower critical value is -2.1199 The upper critical value is 2.1199. (Round to four decimal places as needed.)
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To calculate the tSTAT, we need the standard error (SE). However, the standard error is not provided in the question. If we assume that the standard error is 1.6 (as it's the only other number provided), then the tSTAT would be calculated as b1/SE = 4.5/1.6 = Show more…
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