Answer: t-statistic > t-critical, we reject the null hypothesis.
Therefore, we conclude that kaiser claim is valid.
Explanation:
In this question,
Null hypothesis, [tex]H_{0}[/tex] : Actual cost of rehabilitation is greater than $28,500
Alternative Hypothesis, [tex]H_{a}[/tex] : 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
[tex]H_{0}[/tex]: u > 28500 ⇒ Kaiser claims is not valid
[tex]H_{a}[/tex]: u ≤ 28500 ⇒ Kaiser claims is valid
t - statistic = [tex]\frac{\bar{X} - u}{\frac{SD}{\sqrt{n} } }[/tex]
= [tex]\frac{30885 - 28500}{\frac{1123}{\sqrt{45} } }[/tex]
= 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.
