Mfort Company claims that the average medical claim submitted for services by th
ID: 2922526 • Letter: M
Question
Mfort Company claims that the average medical claim submitted for services by their employees exceeds $500.00. You believe this estimate is too high. You sample 28 claims. These claims have an average of $520 with a standard deviation of $50.00. With this data, evaluate the company’s claim and respond to the questions below. Use an alpha of .05. a. State the null hypothesis________________________________________ b. State the alternative hypothesis__________________________________ c. State the critical value___________________________________________ d. State the computed value_________________________________________ e. State the decision_______________________________________________ f. State the conclusion_____________________________________________ g. State the p-value. _______________________________________________ h. Are you at risk of a Type I or II error___
Explanation / Answer
Given that,
population mean(u)=500
sample mean, x =520
standard deviation, s =50
number (n)=28
null, Ho: <500
alternate, H1: >500
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.703
since our test is right-tailed
reject Ho, if to > 1.703
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =520-500/(50/sqrt(28))
to =2.117
| to | =2.117
critical value
the value of |t | with n-1 = 27 d.f is 1.703
we got |to| =2.117 & | t | =1.703
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.1166 ) = 0.02183
hence value of p0.05 > 0.02183,here we reject Ho
ANSWERS
---------------
null, Ho: =500
alternate, H1: >500
test statistic: 2.117
critical value: 1.703
decision: reject Ho
p-value: 0.02183
type I error