The kaiser medical foundation claims that the cost to rehabilitate a football player following a head injury is at most $28,500. to test this claim a researcher surveys the medical billing records of 45 football players who were treated for head injuries. the average cost for rehabilitation in this randomly selected sample is $30,885 with a standard deviation of $1,123. is the actual cost of rehabilitation at most $28,500 as kaiser claims?

t-statistic > t-critical, we reject the null hypothesis.

Therefore, we conclude that kaiser claim is valid.

Explanation:

In this question,

Null hypothesis, : Actual cost of rehabilitation is greater than $28,500

Alternative Hypothesis, : Actual cost of rehabilitation at most $28,500

the medical billing records of 45 football players, n = 45

\bar{X} ⇒  average cost for rehabilitation = $30,885

: u > 28500 ⇒ Kaiser claims is not valid

: u ≤ 28500 ⇒  Kaiser claims is valid

t - statistic =

=

= 14.25

From the t- distribution, with degree of freedom = n-1 ⇒ 45-1 = 44 and level of significance 0.05

t-critical value = 1.6802

So,

t-statistic > t-critical, we reject the null hypothesis.

Therefore, we conclude that kaiser claim is valid.