Answer:
Now we can find the degrees of freedom:
Now we can calculate the p value with the alternative hypothesis using the following probability:
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed
Step-by-step explanation:
Information given
represent the sample mean
represent the sample standard deviation
sample size
represent the value to verify
t would represent the statistic
represent the p value
System of hypothesis
We want to verify if shoppers participating in the loyalty program spent more on average than typical shoppers (120) , 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:
Now we can find the degrees of freedom:
Now we can calculate the p value with the alternative hypothesis using the following probability:
Using a significance level of 0.01 or 1% we have enough evidence to FAIL to reject the null hypothesis and we can conclude that shoppers participating in the loyalty program NOT spent more on average than typical shopper at this significance level assumed