3. Assume that, on average, students at Okanagan College score 65% on their stat

Question

3. Assume that, on average, students at Okanagan College score 65% on their statistics final exam with population standard deviation 7%. Suppose that our class (assume n = 30) writes their final exam and earns a mean score 72%. If scores are independent and roughly normally distributed, do the following: (a) Create a 95% confidence interval for the mean score of our statistics class. (b) Test the hypothesis that the mean score in our statistics class is different from the typical mean by interpreting a 99% confidence interval for the mean score of our statistics class. (Be sure to show all steps of the hypothesis test for full marks.)
3. Assume that, on average, students at Okanagan College score 65% on their statistics final exam with population standard deviation 7%. Suppose that our class (assume n = 30) writes their final exam and earns a mean score 72%. If scores are independent and roughly normally distributed, do the following: (a) Create a 95% confidence interval for the mean score of our statistics class. (b) Test the hypothesis that the mean score in our statistics class is different from the typical mean by interpreting a 99% confidence interval for the mean score of our statistics class. (Be sure to show all steps of the hypothesis test for full marks.)
3. Assume that, on average, students at Okanagan College score 65% on their statistics final exam with population standard deviation 7%. Suppose that our class (assume n = 30) writes their final exam and earns a mean score 72%. If scores are independent and roughly normally distributed, do the following: (a) Create a 95% confidence interval for the mean score of our statistics class. (b) Test the hypothesis that the mean score in our statistics class is different from the typical mean by interpreting a 99% confidence interval for the mean score of our statistics class. (Be sure to show all steps of the hypothesis test for full marks.)

Explanation / Answer

(a) population mean p = 65% and standerd deviation p= 7%

Mean of the sample s= 72%

so for95% confidence score Z - value = mean +- 1.96 * sd/n = 72% +- 1.96 * 7/30

= (69.495, 76.505)

(b) Nulll hypothysis : H0 : s = p

Alteernativee hypothesis : H1 : s p

so for creating 99% CI for our statistics class.Difference in mean = 72 - 65 = 7%

Z- value for 99% confidence interval = 2.575

so value of zs = 2.575 * 7/30 = 3.290

so, value of zs < s - p

Som by this we can say that mean score of our stastics class is diffrent from the typical mean of university.

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