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?

750 601    1244 572 568 501

Answer 1

The hypothesis being tested is:

Null Hypothesis,H₀: µ =1000

Alternate Hypothesis,H_a: µ <10000

s=276.199

x bar=(750+601+1244+572+568+501)/6=706

The test statistic, t = (x - µ)/s/√n

t=(706-1000)/(276.199/√6)

=-2.607

P value= 0.0239

Conclusion:

Since P value>alpha(0.01). We fail to reject the null hypothesis. There is not sufficient evidence to prove that the sample is from a population with a mean less than 1000 hic.