Question

A college observed that the passing rate for students in their developmental mathematics classes was 66%. As a result, the mathematics department is piloting a computer learning system in their developmental math classes. The advertisers for the learning system promise it will improve pass rates. The college will only have to pay for the program if they decide to continue using it after this semester.

a)Write the null and alternative hypothesis in words. (2 points)

b)In this context, what would a Type I error be?(2points)

c)In this context, what would a Type II error be?(2 points)

d)What type of error would the math department consider more serious? Explain. (3 points)

Answer 1

Ans ) a) according to question , the null and alternate hypotheses are :

H₀ : p = 66%

H_A : p > 66% .

that is a right - tailed test .

where , p is the passing rate of students in their developmental mathematics classes .

b) Type of I error is the probabillity of rejecting a true null hypothesis . So , in this context , we reject the passing rate of students in their developmental mathematics classes is 66% which is true and accept that the passing rate is increased which infact has not increased .

c) probability of type II error is probability of accepting the false null hypothesis . So , in this context , we accept that the passing rate of students in their developmental mathematics classes is 66% which is false and which infact the passing rate is increased .

d) Type II error would the math department consider more serious , because we will accept the false null hypothesis and reject the true claim that the passing rate of students in their developmental mathematics classes is greater than 66% .

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THANKYOU .