Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a .05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

747 694 1175 642 573 471

Answer 1

sr.no.	x	x-x̅	(x-x̅)^2
1	747	30	900
2	694	-23	529
3	1175	458	209764
4	642	-75	5625
5	573	-144	20736
6	471	-246	60516
Total	4302		298070
mean=x̅	Total/6
x̅=	717

of = 0.05 Test that the sample is from a population with a mean less than Dit Hou = 1000 EH, ll 2 1000 1000 hic NS 1 2 [x = 4302 n=6 x= [X = 4302 6 Z(X-)2 = 2980 to 717 S= (x-)? 298070 = 59614 = 244.16 -) 5 - 283 test statistic t = x-l = 717 - 1000 1-slun 244. 16186 t = -2.84 244.16/244949 - 283 99.67781 • p-value = p (tn-i<t)=P(to-1 <-2.84) - Plts L-284) 21 = P(ts> 2.84) = 1 - Plts 2.84) = 1 – 0.9819 P-valve = 0.018/ Decision : Here Reject Hor if p-value <a p-value =0.0181 <=0.05 Reject Hoi conclusion There is sufficient evidence to support that the sample is from a population with a mean 1ooo hic. less than