Question

assume that a sample 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 0.01 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?
620 648 1024 579 520 571
what are the hypotheses?
a. ( h_0:mu = 1000 ) hic ( h_1:mugeq1000 ) hic
b. ( h_0:mu = 1000 ) hic ( h_1:mult1000 ) hic
c. ( h_0:mugt1000 ) hic ( h_1:mult1000 ) hic
d. ( h_0:mu = 1000 ) hic ( h_1:mugeq1000 ) hic

Explanation:

Step1: Understand the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. In hypothesis testing for a population mean, when we are testing a claim about the mean, the null hypothesis is usually of the form \(H_0:\mu=\) some value. Here, the value we are comparing to is \(1000\) hic. So \(H_0: \mu = 1000\) hic.

Step2: Understand the alternative hypothesis

The claim is that the sample is from a population with a mean less than \(1000\) hic. The alternative hypothesis \(H_1\) is the statement we are trying to find evidence for. So \(H_1: \mu < 1000\) hic.

For option A, the null hypothesis \(H_0:\mu < 1000\) hic is incorrect because the null hypothesis should be an equality statement for a hypothesis test about a population mean. For option C, \(H_0:\mu> 1000\) hic is wrong as the null hypothesis is not an inequality. For option D, \(H_1:\mu\geq1000\) hic is incorrect as it does not match the claim of the mean being less than \(1000\) hic.

Answer:

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