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?

Answer 1

Explanation:

The question is incomplete. The missing part is shown in the comment box.

Mean = (697 + 759 + 1266 + 621 + 569 + 432)/6 = 724

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (697 - 724)^2 + (759 - 724)^2 + (1266 - 724)^2+ (621 - 724)^2 + (569 - 724)^2 + (432 - 724)^2 = 415616

Standard deviation = √415616/6 = 263.2

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 1000

For the alternative hypothesis,

µ > 1000

It is a right tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t. The test statistic, t would be calculated with the formula below

Since n = 6

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

t = (x - µ)/(s/√n)

Where

x = sample mean = 724

µ = population mean = 1000

s = samples standard deviation = 263.2

t = (724 - 1000)/(263.2/√6) = - 2.57

We would determine the p value using the t test calculator. It becomes

p = 0.025

From the t distribution table, the critical value is 2.571

Since alpha, 0.05 > than the p value, 0.025, then we would reject the null hypothesis.

Therefore, at a 5% level of significance, the results do not suggest that all of the child booster seats meet the specified​ requirement.

The results suggests that the safety requirement for the hic measurement should be more than 1000 hic.