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?

831    

804    

1206     

669    

670    

590

  

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 1000
Alternative Hypothesis: 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 = (795 - 1000)/(220.8275/sqrt(6))
t = -2.274

P-value Approach
P-value = 0.0360
As P-value < 0.05, reject the null hypothesis.

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