Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
c) The degrees of freedom are given by:
Now we can calculate the p value, since we are conducting a two tailed test:
Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes
Step-by-step explanation:
Information provided
represent the sample mean
in minutes
represent the 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
Part a
We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Part b
Since we don't know the population deviation the statistic is given by:
(1)
Replacing the info given we got:
Part c
The degrees of freedom are given by:
Now we can calculate the p value, since we are conducting a two tailed test:
Since the p value is lower than the significance level of we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes