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 loss 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
identify the test statistic.
( t=-3.34 ) (round to three decimal places as needed.)
identify the p - value.
the p - value is 0.0103
(round to four decimal places as needed.)
state the final conclusion that addresses the original claim.
( h_0 ). there is evidence to support the claim that the sample is from a population with a mean less than 1000 hic.
reject
fail to reject

Explanation:

Step1: Determine the decision rule

Compare the P - value with the significance level. Here, the significance level \(\alpha = 0.05\).

Step2: Make a decision

Since the P - value \(0.0103<0.05\), we reject the null hypothesis \(H_{0}\).

Answer:

Reject \(H_{0}\). There is sufficient evidence to support the claim that the sample is from a population with a mean less than 1000 hic.