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 0.010.01 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?

645645     602602     12201220     591591     579579     539539

b) Identify the test statistic.

c)Identify the​ P-value.

Answer 1

the necessary calculation table:-

hic measurement (x)	x2
645	416025
602	362404
1220	1488400
591	349281
579	335241
539	290521
sum=4176	sum=3241872

sample size (n) = 7

a).hypothesis:-

b).test statistic be:-

c). df = (n-1 )= (6-1) = 5

p value :-

[ in any blank cell of excel type =T.DIST(-2.875,5,TRUE) type enter]

decision:-

p value = 0.0174 > 0.01 (alpha)

so, we fail to reject the null hypothesis.

we conclude that,  there is not sufficient evidence to suggest that all of the child booster seats meet the specified​ requirement at 0.01 leval of significance.

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