Question 4Answer part D only!! To test $ H_0: \mu = 40 $ versus $ H_1: \mu < 40 $, a random sample of size $ n = 25 $ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.**(a)** If $ \bar{x} = 37.4 $ and $ s = 13.6 $, compute the test statistic.\[ t_0 = -0.956 \] (Round to three decimal places as needed.)**(b)** If the researcher decides to test this hypothesis at the $ \alpha = 0.05 $ level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given.\[ \text{Critical Value: } -1.711 \] (Round to three decimal places. Use a comma to separate answers as needed.)**(c)** Draw a t-distribution that depicts the critical region. Choose the correct answer below.- Option A shows a distribution with the critical region on the right tail.- **Option B** shows a distribution with the critical region on the left tail, marked at $-t_{\alpha}$.- Option C shows a distribution with critical regions on both tails.**(d)** Will the researcher reject the null hypothesis?- $ \circ $ A. No, because the test statistic does not fall in the critical region.- $ \circ $ **B. No, because the test statistic falls in the critical region.**- $ \circ $ C. Yes, because the test statistic does not fall in the critical region.- $ \circ $ D. Yes, because the test statistic falls in the critical region.

Given: n= 25.0 ,x̄= 37.4 ,s= 13.6 µ= 40.0 ,significance level(∝)= 0.05 ,degree of freedom= 24.0 define hypothesis;- Null Hypothesis,H0:µ= 40.0 Alternative hypothesis,H1:µ< 40.0 (left tailed test) TTest Statistic. Under the H0, the test statistic is: t=(x̄-µ)/(s/√(n-1)) t=( 37.4 - 40.0 )/( 13.6 / √ 25.0 ) t= -0.9559 t-critical=-1.711 d)conclusion: so here we can see that test statistic(t) > t-critical fail to reject null hypothesis(H0)(accept H0). conclude that the There is not enough evidence to support the claim.hence option A is correct. "No, because the test statistic does not fall in the critical region".