In a simple linear regression based on 27 observations, it is found that b_1 = .
ID: 3160279 • Letter: I
Question
In a simple linear regression based on 27 observations, it is found that b_1 = .46 and se(b_j) = .26. Consider the hypotheses (Use Table 2): H_0: beta_1 lessthanorequalto 0 and H_A: beta_1 > 0 At the 5% significance level, find the critical value(s). (Round your answer to 3 decimal places.) Critical value________Calculate the value of the appropriate test statistic. (Round your answer to 2 decimal places.) Test statistic________At the 5% significance level, what is the conclusion to the hypothesis test? Does the explanatory variable have a positive effect on y? Reject H_0; the explanatory variable has a positive effect on y. Do not reject H_0; the explanatory variable does not have a positive effect on y. Reject H_0; the explanatory variable does not have a positive effect on y. Do not reject H_0; the explanatory variable has a positive effect on y.Explanation / Answer
Critical value is defined as a cut off value which can be used to determine whether to reject or accept null hypothesis. If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favour of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected.
For the above problem, the test statistics is
t(test statistics) = b1/S.E(b1)
and the critical value is t,n-1 which is value of t distribution for level of significance and n-1 degree of freedom, where n is the number of observations.
Here, n=27 , = 0.05 ( because question ask for 5% level of significance) , b1 = 0.46 , S.E(b1) = 0.26