Use the following for questions 3 and 4. Information given about a new make of a

Question

Use the following for questions 3 and 4. Information given about a new make of automobile states that the mean highway gas mileage is 28 miles per gallon. A consumer’s group did a survey of 36 owners of this make of automobile to find out what the mileage they actually got. They used their data to test the hypotheses H0: = 28, Ha: < 28 where is the mean highway gas mileage for this make of automobile. With a sample mean of 26 and sample standard deviation of 5, the pvalue turns out to be p = .0082. What hypothesis should we accept?

a. accept H0: = 28

b. accept Ha: less than 28

If the sample were 25 instead of 26, would the new p-value be less than or greater than .0082?

a. The new p-value would be less than .0082.

b. The new p-value would be greater than .0082.

Explanation / Answer

Set Up Hypothesis
Null, H0: U>28
Alternate, H1: U<28
Test Statistic
Population Mean(U)=28
Sample X(Mean)=26
Standard Deviation(S.D)=5
Number (n)=36
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =26-28/(5/Sqrt(36))
to =-2.4
| to | =2.4
Critical Value
The Value of |t | with n-1 = 35 d.f is 1.306
We got |to| =2.4 & | t | =1.306
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -2.4 ) = 0.01092
Hence Value of P0.1 > 0.01092,Here we Reject Ho

[ANSWER]
accept Ha: less than 28

When the sample were 25 instead of 26
Test Statistic
Population Mean(U)=28
Sample X(Mean)=25
Standard Deviation(S.D)=5
Number (n)=36
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =25-28/(5/Sqrt(36))
to =-3.6
| to | =3.6
P-Value :Left Tail -Ha : ( P < -3.6 ) = 0.00049

[ANSWER]
a. The new p-value would be less than .0082

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