Answer:
The degrees of freedom are given by:
The p value for this case would be given by:
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis
Step-by-step explanation:
Information given
represent the sample mean
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
Hypothesis to verify
We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case is given by:
(1)
Replacing we got:
The degrees of freedom are given by:
The p value for this case would be given by:
If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis