Question

assume that a simple random sample has been selected from a normally distributed population and test the give claim. identify the null and alternative hypotheses, test statistic, p - value, and state the final conclusion that addi the original claim.
a safety administration conducted crash tests of child booster seats for cars. listed below are results from those 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 population with a mean less than 1000 hic. do the results suggest that all of the child booster seats meet the specified requirement?
632 583 1112 604 512 625
what are the hypotheses?
a. ( h_0:mu = 1000 ) hic ( h_1:mugeq1000 ) 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:mu < 1000 ) hic

Explanation:

Step1: Determine the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The claim is that the population mean \(\mu< 1000\) hic. So, \(H_0:\mu = 1000\) hic (the status - quo, no difference from the value we are comparing to) and \(H_1:\mu<1000\) hic (the claim we are testing).

Step2: Analyze the options

• Option A: \(H_1:\mu\geq1000\) hic is wrong as our claim is \(\mu < 1000\) hic.
• Option B: \(H_0:\mu>1000\) hic is wrong because the null hypothesis should be an equality.
• Option C: \(H_0:\mu < 1000\) hic is wrong as the null hypothesis should be an equality.
• Option D: \(H_0:\mu = 1000\) hic and \(H_1:\mu<1000\) hic is correct.

Answer:

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