23-27 go togehther. If you could show your work and formula used. Thanks. Use th

Question

23-27 go togehther. If you could show your work and formula used. Thanks. Use the following information to answer the next 5 questions (23-27): Last year it took students and average of 80 minutes to finish the final exam. Suppose the average time a sample of 20 students takes to finish this year's final exam has a mean of85 minutes and standard deviation of 15. We see that a histogram of the data shows no signs of skewness and a BoxPlot shows no outliers. We want to run a hypothesis test to see if this years exam is significantly longer than last year's. (use a 0.01) 23) What are the correct hypotheses for this test? a) Ho: 80 c) Ho: 80 Ha: uz 80 Ha: H 800 b) Ho: H 80 d) Ho: u z 80 Ha: H 80 Ha: H- 800 24) What is your resulting Test Statistic? a) -1.49 c) 13.33 b) 1.49 d) 2.0572 25) What Critical value should we use? a) 2.539 c) 2.575 b) 1.96 d) 2.861 26) Based on the information above, and using your table, what do you estimate the p-value would be? a) Between 0.1 and 0.2 c) Between 0.001 and 0.005 b) Between 0.025 and 0.05 d) Between 0.05 and 0.1 27) What is your resulting decision? a) Reject the Null Hypothesis, we have significant evidence to conclude that this year's exam is longer than last years b) Reject the Null Hypothesis, we do not have significant evidence to conclude that this year's exam is longer than last years c) Fail to reject the Null Hypothesis, we do not have significant evidence to conclude that this year's exam is longer than last years d) Fail to reject the Null Hypothesis, we have significant evidence to conclude that this years exam is longer than last years

Explanation / Answer

23) Below are the null and alterante hypothesis
H0: mu = 80
H1: mu > 80
Option (c) is correct

24)
Test statistics, t = (85 - 80)/(15/sqrt(20)) = 1.4907
Option (B) is correct

25)
For significance level of 0.01
Critical value = 2.5395
Option (A) is correct

26)
p-value for the calcuated value of test statistics
p-value = 0.0762
Option (D) is correct

27)
As p-value is greater than significance level of 0.01, we fail to reject the null hypothesis.
Option (C) is correct

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