Question

The Department of Statistics at Great Ivy University offers Stat 101 – Introductory Statistics with the use of a calculator. The Department wants to see if students in Stat 101 will benefit more by adding a new software package to Stat 101 versus keep using only the calculator. Five of 10 sections chosen at random will be required to rent the software, the other five will not. Re same

(a) Is this a one-tailed or a two-tailed test? Explain.

(b) State the null and alternative hypotheses. (Remember: The null hypothesis is one of no effect, i.e. no difference in exam grades.)

(c) In this context, what would a Type I error be? What are the consequences?

(d) In this context, what would a Type II error be? What are the consequences?

(e) Which error type is more serious? Explain

Answer 1

(a) This is a one tailed test

Note : As we need to see whether exam grades with software package are better than that of with calculator , thus we need to perform one tailed test .

(b) The null hypothesis is

(there is no difference in exam grades)

and alternative hypothesis is

(exam grades are higher for students with software package )

where are population mean grades of students with software package and calculator respectively .

(c) Type I error is the error of rejecting a true null hypothesis

That is , on the basis of the test we conclude that students with software package performs better than students with calculator , where as in reality there is no significance difference between exam scores .

Consequences : The department adds new software package , which is of no benefit , but increases expenditure

(d)

Type II error is the error of accepting a false  null hypothesis

That is , on the basis of the test we conclude that students with software package performs same as   students with calculator , where as in reality students with software package performs better.

Consequences : The department decides not to add new software package , which if added would have been helpful to students.

(e) In this situation Type II error is more serious . As the new software is not introduced in the department , which would have been helpful to students to learn better and score more .