Question

In the year 2000, the average car had a fuel economy of 23.53 MPG. You are curious as to whether this average is different from today. The hypotheses for this scenario are as follows: Null Hypothesis: μ = 23.53, Alternative Hypothesis: μ ≠ 23.53. You perform a one sample mean hypothesis test on a random sample of data and observe a p-value of 0.0113. What is the appropriate conclusion? Conclude at the 5% level of significance.

A. We did not find enough evidence to say a significant
difference exists between the true average fuel economy today and
23.53 MPG.

B. The true average fuel economy today is significantly greater
than 23.53 MPG.

C.The true average fuel economy today is significantly different
from 23.53 MPG.

D. The true average fuel economy today is significantly less than
23.53 MPG.

E. The true average fuel economy today is equal to 23.53 MPG.

Answer #1

In testing of hypothesis , if the p value is less than ,the reject the null hypothesis

Here, given the null hypothesis is Ho :

and the alternative hypothesis i s H1 :

p value = 0.0113

and level of significance =5%= 0.05

since the p value is less than , therefore reject the null hypothesis

and accepting the alternative hypothesis

ie the conclusion is

c) the true average fuel economy today is significantly different from 23.53 MPG

In the year 2000, the average vehicle had a fuel economy of
24.84 MPG. You are curious as to whether the average in the present
day is different from the historical value. The hypotheses for this
scenario are as follows: Null Hypothesis: μ = 24.84, Alternative
Hypothesis: μ ≠ 24.84. A random sample of 37 vehicles shows an
average economy of 25.99 MPG with a standard deviation of 4.915
MPG. What is the test statistic and p-value for this test?

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