The mathematics department at a community college tested a n

The mathematics department at a community college tested a new delivery method for developmental mathematics courses. They want to see if the mean score on the final exam using the new method is higher than the known mean score on the final exam of 67.8% using traditional delivery methods.

a.) State the random variable in words?

b.) State the parameter in words. Include the correct symbol for the parameter.

c.) State the null hypothesis. Use correct notation.

d.) State the alternative hypothesis. Use correct notation.

e.) Identify what a type I error would be in this problem.

f.) Identify what a type II error would be in this problem.

g.) State the consequences of a type I error for the mathematics department.

h.) State the consequences of a type II error for the mathematics department.

i.) What alpha level should they use and why?

j.) If the department runs a hypothesis test, and finds the p-value is 0.123. What conclusion should they make?

k.) Based on your conclusion, what is the interpretation?

l.) Using the alpha level that you chose, what could they do to lower their chance of a type II error?

Solution

The null hypothesis is:

H0:=67.8%

Against the alternative hypothesis

H0:>67.8%

The alpha level should be 0.05.

If the P value is 0.123, which is greater than alpha=0.05, fail to reject the null hypothesis.

Thus, the test is not statistically significant.