Answer:
The degrees of freedom are given by:
The p value would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:
a. No
Step-by-step explanation:
Information given
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic
represent the p value
Hypothesis to test
We want to check if the true mean is different from 75, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing we got:
The degrees of freedom are given by:
The p value would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 75 and the best option would be:
a. No