A local official is attempting to determine if the regional price of unleaded re
ID: 2958666 • Letter: A
Question
A local official is attempting to determine if the regional price of unleaded regular gasoline exceeds the national average of $3.09 per gallon. She surveys 28 local stations recording the gasoline price on a single day. The average value was $3.14 with a standard deviation of $0.54, a minimum of $2.91 and a maximum of $3.25.
A. Define the hypotheses for this measurement in (1) statement form, and (2) equation form.
B. In the context of the hypotheses in part A, interpret the consequences of making a Type I error, and a Type II error.
Problem 4:
An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $71.81.
(a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket? State your hypotheses and decision rule.
(b) Is this a close decision?
Explanation / Answer
A. Define the hypotheses for this measurement in
(1) statement form
Ho: the regional price for regular gas is less than or equal to $3.09
Ha: the regional price for regular gas is greater than $3.09
(2) equation form
H0: $3.09
Ha: > $3.09
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B Type I error:
This means we reject the null hypothesis when it is true.
We say that the gas costs more than $3.09, when it actually doesn't.
Type II error:
This means we do not reject the null hypothesis when we should have rejected it.
We say that the gas doesn't exceed $3.09, but it actually does.
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Problem4
(A) The test hypothesis is
Ho:<=250
Ha:>250
Given a=0.05, the critical value is |t(0.05,df=n-1=24)|=1.711
The test statistic is
t=(xbar-)/(s/n)
=(275.66-250)/(78.11/sqrt(25))
=1.643
Since t=1.643<1.711, we do not reject Ho.
(b) yes.
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