Question

Complete the following hypothesis test: Ho: u = 52, H: 4 < 52, a = 0.01 using the data below. 44 46 49 55 58 47 47 50 52 51 46 40 (a) Find t. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion. O Fail to reject the null hypothesis. There is significant evidence that the mean is less than 52. O Reject the null hypothesis. There is significant evidence that the mean is less than 52. O Fail to reject the null hypothesis. There is not significant evidence that the mean is less than 52. O Reject the null hypothesis. There is not significant evidence that the mean is less than 52. You may need to use the appropriate table in Appendix B to answer this question. Need Help? Read It Watch It Talk to a Tutor

Answer 1

sr.no.	x	x-x̅	(x-x̅)^2
1	44	-4.75	22.5625
2	46	-2.75	7.5625
3	49	0.25	0.0625
4	55	6.25	39.0625
5	58	9.25	85.5625
6	47	-1.75	3.0625
7	47	-1.75	3.0625
8	50	1.25	1.5625
9	52	3.25	10.5625
10	51	2.25	5.0625
11	46	-2.75	7.5625
12	40	-8.75	76.5625
Total	585		262.25
mean=x̅	Total/12
x̅=	48.75

d=0.01 1 { x = 585 Hoi u=52 Elx-x2 = 262.25 V Ha : 452 x = {x - 582 48.75 s={1x-xgr - 262.25 = -8? = 262,25 23.84091 4.883 3,25 test statistic t = X-4 = 48.75-52 slun 4.883 / 112 t = -2,31 - 2,31 -3.25 4.883/3,4641 P-value=pltnult) =P(t12-1 2-2,31) = P(til 2-2,31) = P(tu > 2131) 1- pitu [2.31) = 0.9794 p-value = 0.0206 Decision Reject Ho it praele ca Hese fail to reject Ho. pvalue=0.0206 >2=0.01 Conclusion Fail to reject null hypothesis. There is not significant evidence that the mean is less than 52.