Question

assume that a simple random sample has been selected from a normally distributed population and test the claim. identify the null and alternative hypotheses, test statistic, p - value, and state the final conclusion that the original claim.
a safety administration conducted crash tests of child booster seats for cars. listed below are results from with the measurements given in hic (standard head injury condition units). the safety requirement is that the measurement should be less than 1000 hic. use a 0.05 significance level to test the claim that the sample is 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
c. ( h_{0}: mu<1000 ) hic ( h_{1}: mu geq 1000 ) hic
d. ( h_{0}: mu = 1000 ) hic ( h_{1}: mu<1000 ) hic
identify the test statistic.
( t = - 3.635 ) (round to three decimal places as needed.)
identify the p - value.
the p - value is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the sample size \(n\)

The data set has \(n = 6\) values.

Step2: Determine the degrees of freedom \(df\)

The degrees of freedom for a one - sample \(t\) - test is \(df=n - 1\). So, \(df=6 - 1=5\).

Step3: Use the \(t\) - distribution table or technology to find the \(P\) - value

Since this is a left - tailed test (because \(H_1:\mu<1000\)) and \(t=-3.635\) with \(df = 5\). Using technology (such as a TI - 84 Plus: tcdf(-1000,-3.635,5)), we find the \(P\) - value.

Answer:

The \(P\) - value is \(0.0073\)