Answer:
The degrees of freedom are given by:
The p value for this case is given by:
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense
Step-by-step explanation:
Information given
represent the sample mean
represent the sample standard deviation
sample size
represent the value to verify
represent the significance level
t would represent the statistic (variable of interest)
represent the p value
Hypothesis to est
We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case is given by;
(1)
Replacing the info given we got:
The degrees of freedom are given by:
The p value for this case is given by:
Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense