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As we know that :
so, over here
plugging the value of i² as -1
Answer:
The p value would be:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we cna conclude that the true mean is less than 60 at 10% of significance.
Step-by-step explanation:
Information given
represent the sample mean of interest
represent the sample standard deviation
sample size
represent the value to check
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test
System of hypothesis
we want to check if the true mean is lower than 60, so thn the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replcing into the formula we got:
P value
The degrees of freedom are given by:
The p value would be:
Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is less than 60 at 10% of significance.