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? 644 612 1138 590 557 683 what are the hypotheses? a. ( h_{0}:mu>1000 ) hic ( h_{1}:mu<1000 ) hic b. ( h_{0}:mu = 1000 ) hic ( h_{1}:mu<1000 ) hic c. ( h_{0}:mu<1000 ) hic ( h_{1}:mugeq1000 ) hic d. ( h_{0}:mu = 1000 ) hic ( h_{1}:mugeq1000 ) hic

Explanation:

Step1: Recall the definition of null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. Here, the claim is that the population mean \(\mu< 1000\) hic.

Step2: Analyze each option

• Option A: The null hypothesis \(H_0:\mu > 1000\) hic is incorrect because the null hypothesis should be a statement of equality.
• Option B: \(H_0:\mu=1000\) hic (null hypothesis, statement of equality) and \(H_1:\mu < 1000\) hic (alternative hypothesis, the claim we test) is correct.
• Option C: The null hypothesis \(H_0:\mu < 1000\) hic is incorrect as the null hypothesis must have an equality.
• Option D: The alternative hypothesis \(H_1:\mu\geq1000\) hic is not the claim (the claim is \(\mu < 1000\) hic).

Answer:

B. \(H_0:\mu = 1000\) hic, \(H_1:\mu < 1000\) hic