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 0.05 0.05 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? 783 761 1184 633  601 694

Answer 1

Claim: The safety requirement is that the hic measurement should be less than 1000 hic.

Sample size = n = 6

Sample mean = = 776

Standard deviation = s = 211.9132

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 6 - 1 = 5

P-value = P(T < - 2.59) = 0.0244

P-value < 0.05 we reject null hypothesis.

Conclusion: The safety requirement is that the hic measurement should be less than 1000 hic.