Answer the following questions showing all work. Full credit will not be given t

Question

Answer the following questions showing all work. Full credit will not be given to answers without work shown. If you use Minitab Express or StatKey include the appropriate output (copy + paste). If you do hand calculations show your work using the Word equation editor. Clearly identify your final answers. Output without explanation will not receive full credit and answers with no output or explanation will not receive full credit. Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board.

1. A STAT 200 instructor wants to compare the final exam scores of students taught using two different curricula. She obtains a sample of 600 students. She randomly assigns 300 students to a traditional curriculum and 300 students to a new curriculum. It is hypothesized that the new curriculum will lead to higher scores. If there is no significant difference, then she will continue to teach using the older curriculum. If there is a significant difference, then she will switch to the new curriculum. [64 points]

A. State the null and alternative hypotheses that the instructor should test. Use m1 to denote the mean final exam score of students in the traditional curriculum group and m2 to denote the mean final exam score of students in the new curriculum group.

B. What does a Type I error mean in this situation? What are the consequences of making a Type I error here?

C. What does a Type II error mean in this situation? What are the consequences of making a Type II error here?

D. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your

Explanation / Answer

A. Here the null hypothesis is, H0: the average scores of new

curriculum and traditional curriculum are same i.e. m1 = m2.

The alternative hypothesis is, H1: m2 > m1. (Ans).

B. In this case Type I error will be rejecting H0 when it is true,

i.e. concluding that the average score of new curriculum is

higher than the traditional curriculum when it is not.

Thus, it will result in the instructor implementing the new

curriculum. (Ans).

C. Type II error means fail to reject H0 when it is false i.e.

concluding that the new curriculum is not leading to higher

scores when actually it is leading to higher scores. It means

that the instructor will continue with the old curriculum. (Ans).

D. In this case both the errors are equally serious, as either

way the instructor missed the opportunity to move into a

curriculum which will yield higher scores. (Ans).

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