A safety administration conducted crash tests of child booster seats for cars. l

Question

A safety administration conducted crash tests of child booster seats for cars. listed are the results from thise tests, with the measurements given in hic (standard head injury condition units). 771, 722, 1284, 672, 607, 492. Assuming the hic measurements of child booster seats is normally distributed, use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. identify the null and alternative hypothesis, test statistic, p-value, and state the final conclusion that addresses the original claim.

Explanation / Answer

Here, we have to use one sample t test for the population mean. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: µ = 1000

Alternative hypothesis: Ha: µ < 1000

This is a one tailed test. This is a lower tailed or left tailed test.

We are given a level of significance or alpha value as 1% or 0.01.

Sample size = n = 6

Degrees of freedom = n – 1 = 6 – 1 = 5

From the given sample, we have

Sample mean = Xbar = 758

Sample standard deviation = SD = 275.35

The test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [SD/sqrt(n)]

Test statistic = t = (758 – 1000) / [275.35/sqrt(6)]

Test statistic = t = -2.1528

P-value = 0.0420 (By using t-table or excel)

Alpha value = 0.01

P-value > Alpha value

So, we do not reject the null hypothesis.

We conclude that there is no sufficient evidence that the population mean is less than 1000 hic.

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