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 0.01 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? 741     681     1298     611     564     551

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1000
Alternative Hypothesis, Ha: μ < 1000

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (741 - 1000)/(282.1978/sqrt(6))
t = -2.248

P-value Approach
P-value = 0.0372
As P-value >= 0.01, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the sample is from a population with a mean less than 1000 hic