Believe it or not, while writing this assignment, I traveled forward in time and

Question

Believe it or not, while writing this assignment, I traveled forward in time and collected a random sample of 25 submissions for this assignment The names on the assignments did not survive the return time-trip, but I could still calculate the average total score on the sampled assignments, which was 10, and their sample standard deviation, which was 1.8. On the basis of this information: Find a 95% confidence interval for the actual average score mu for the entire class. Construct a 99/95 tolerance interval for your score on this assignment (i.e., an interval that includes 99% of possible observations with 95% confidence). Discuss any issues. While collecting the sample, I met my future self, who told me the actual mean and standard deviation of scores for all submitted assignments. Unfortunately, the time-travel sickness I experienced on my return trip to the present meant I was only able to remember the standard deviation, which was 2.0. Given this information, how would you change the interval you calculated in part (a), if at all?

Explanation / Answer

Here we have to find 95% and 99% confidence interval.

sample size = n = 25

Xbar = 10

sample standard deviation = s = 1.8

c = confidence level = 95% = 0.95

This we can find by using TI-83 calculator.

STAT --> TESTS --> 8:TInterval --> ENTER --> Highlight on Stats --> ENTER --> Input all the values --> Calculate --> ENTER

95% confidence interval for population mean is (9.257, 10.743).

Similarly we can find 99% confidence interval by using C-level = 0.99.

99% confidence interval for population mean is (8.9931, 11.007).

Now we have to find 95% and 99% confidence interval for population mean when standard deviation = 2.0

By using TI_83 calculator we can find confidence interval for population mean.

95% confidence interval for population mean is (9.1744, 10.826).

99% confidence interval for population mean is (8.8812, 11.119).

And higher confidence has wider confidence interval whileas lower confidence has narrower confidence interval.

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