Answer:
Null hypothesis:
Alternative hypothesis:
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.
Step-by-step explanation:
Information provided
represent the sample mean for the MPG of the cars
represent the population standard deviation
sample size of cars
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test
Hypothesis
We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation the statistic is given by:
(1)
Calculate the statistic
Replacing we have this:
Decision
Since is a two tailed test the p value would be:
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.