Problem
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? What are the hypotheses? A. $\mathrm{H}_{0}: \mu=1000$ hic $\mathrm{H}_{1}: \mu<1000$ hic c. \[ \begin{array}{l} H_{0}: \mu=1000 \text { hic } \\ H_{1}: \mu \geq 1000 \text { hic } \end{array} \] B. $\mathrm{H}_{0}: \mu>1000$ hic $\mathrm{H}_{1}: \mu<1000$ hic D. $\mathrm{H}_{0}: \mu<1000$ hic $\mathrm{H}_{1}: \mu \geq 1000$ hic
Solution
Step 1 ：The question is asking for the null and alternative hypotheses for the given scenario. The null hypothesis is typically a statement of no effect or status quo and the alternative hypothesis is what we are testing against the null hypothesis. In this case, we are testing the claim that the sample is from a population with a mean less than 1000 hic. So, the null hypothesis would be that the mean is equal to 1000 hic and the alternative hypothesis would be that the mean is less than 1000 hic.
Step 2 ：Final Answer: The hypotheses are \(\boxed{H_{0}: \mu=1000 \text{ hic}, H_{1}: \mu<1000 \text{ hic}}\).
