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?

Question

Mathematics

Ishaan Frey

29 July, 19:52

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?

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Sadie Holland · Answer 1

Step-by-step 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.