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Answer:
And the p value would be given by:
And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
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 (variable of interest)
System of hypotheses.
We need to conduct a hypothesis in order to check if the true mean is 33.7 mpg or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
And the p value would be given by:
And since the p value is higher than the significance level we have enough evidence to fail to reject the null hypothesis.