Question

According to the 2016 CCSSE data from about 430,000 community college   students nationwide, about 13.5% of students reported that they “often” or “very often” come to class without completing readings or assignments.

Are the results similar at community colleges in California? Specifically, let’s test the claim that California students are different. Use a 5% level of significance.

Suppose that the CCSSE is given in California to a random sample of 500 students and 10.5% report that they “often” or “very often” come to class without completing readings or assignments.

a) State the hypotheses in words and write a sentence to explain what p represents.

b)Verify that the normal model is a good fit for the distribution of sample proportions.

c) Test the claim by a significance test( 6-steps, show all calculations)

d)State your conclusion.

Answer 1

(A) we have to test the claim that the test the California students are different.

Population proportion is given as p = 13.5/100 = 0.135

Null hypothesis (California students are not different)

Alternate hypothesis (California students are different)

(B) we have to check the conditions for normal model

and , if these conditions are satisfied then we can say it is good for the distribution of sample proportion.

we have sample proportion p(hat) = 10.5/100 = 0.105 and sample size is n = 500

setting the values, we get

and

So, both the conditions are satisfied. Normal model is good for the distribution of the sample proportion

(C) 6 STEP HYPOTHESIS TESTING

STEP 1

Null hypothesis (California students are not different)

Alternate hypothesis (California students are different)

STEP 2

Significance level of the testing is 0.05

STEP 3

Reject null hypothesis when p value is less than 0.05

STEP 4

Calculation for test statistic

Formula for the test statistic is given as

z statistic =

setting the given values from the question

we get

z statistic =

STEP 5

Now, using the z distribution, we can get the corresponding p value for the two tailed hypothesis

p value = 0.049996

P value is less than significance level of 0.05

So, we will reject the null hyothesis.

STEP 6 CONCLUSION

Since the p value is significant, thus we can conclude that at 0.05 level of significance, we have enough evidence to support the claim that california students are different.

(D)

we can conclude that at 0.05 level of significance, we have enough evidence to support the claim that california students are different.