Answer:
a)
So on this case the 95% confidence interval would be given by (25.06;33.74)
b)
If we compare the p value and the significance level given the sample mean
population mean (variable of interest)
represent the population standard deviation
n=10 represent the sample size
95% confidence interval
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (25.06;33.74)
Part b
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
Compute the test statistic
The statistic for this case is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
We can replace in formula (1) the info given like this:
Give the appropriate conclusion for the test
Since is a one side right tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis.