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 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? 748. 796. 1196 650 594. 636

Static test

P value

Answer 1

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

Rejection Region
This is left tailed test, for α = 0.05 and df = 5
Critical value of t is -2.015.
Hence reject H0 if t < -2.015

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (770 - 1000)/(221.7963/sqrt(6))
t = -2.54

P-value Approach
P-value = 0.0259
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the hic measurement should be less than 1000 hic