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 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? 783 761 1184 633 601 694
Claim: The safety requirement is that the hic measurement should be less than 1000 hic.
Sample size = n = 6
Sample mean = = 776
Standard deviation = s = 211.9132
The null and alternative hypothesis is
Level of significance = 0.05
Here population standard deviation is unknown so we have to use
Test statistic is
Degrees of freedom = n - 1 = 6 - 1 = 5
P-value = P(T < - 2.59) = 0.0244
P-value < 0.05 we reject null hypothesis.
Conclusion: The safety requirement is that the hic measurement should be less than 1000 hic.
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