Question

We have learned hypothesis tests

1. for the mean (when population variance is known and when it is unknown)
2. for a percentage
3. to see if the means of two sets of data are the same
4. goodness of fit test
5. test for independence

For each type give a brief example. You do not have to solve the problem you give. Try to come up with a problem on your own

Answer 1

for the mean (when the population variance is known )

- In a class of 40 students, the teacher claims that the average marks are 70 out of 100. You need to test the hypothesis is here claim is true at a given level of significance given the distribution of marks with mean 68 and variance 5 N( 65, 5 ).

for the mean (when the population variance is unknown )

- In a class of 40 students, the teacher claims that the average marks are 70 out of 100. You need to test the hypothesis is here claim is true at a given level of significance and by collecting a sample of size 12.

for a percentage

- In a class of 40 students, the teacher claims that 30% of the students will get grades below C. You need to test the hypothesis is here claim is true at a given level of significance and by collecting a sample of size 12.

to see if the means of two sets of data are the same

- In a class of 40 students, the teacher claims that the average marks of girls and boys are the same. You need to test the hypothesis is here claim is true at a given level of significance given the distribution of marks for boys with mean 68 and variance 5 N( 65, 5 ) and for girls with mean 71 and variance 3 N( 71, 3)

the goodness of fit test

- In a class of 40 students, the teacher claims that the top 10% students get A grade, next 20% gets B,next 30% gets C and remaining gets below D. You need to test the hypothesis is here claim is true at a given level of significance for the observed values A = 5, B = 8, C = 10, Rest = 17

test for independence

- In a class of 40 students, the teacher claims that the gender of the student is independent of whether he will get a grade below C or not. You need to test the hypothesis is here claim is true at a given level of significance for the observed values

	Above C	Below C
Male	7	11
Female	10	12