Answer:
The degrees of freedom are given by:
The p value can be calculated like this:
For this case since the p value is higher than the significance level we have enough evidence to conclude that the true mean for the wait time is not significantly less than 8 minutes
Step-by-step explanation:
Information given
represent the sampke mean in minutes
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
System of hypothesis
For this case we are trying to proof if inspection station advertises that the wait time for customers is less than 8 minutes, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since the population deviation is not known the statistic can be calculated with:
(1)
The statistic for this case is given by:
The degrees of freedom are given by:
The p value can be calculated like this:
For this case since the p value is higher than the significance level we have enough evidence to conclude that the true mean for the wait time is not significantly less than 8 minutes