Question

9.55 The U.S. Department of Education reports that 40% of full-time college students are employed while attending college. (Data extracted from The Condition of Education 2012,ncesed.gov/pubs2012/2012045.pdf.) A recent survey of 60 full-time students at a university found that 25 were employed.

A) Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of full-time students at the university is different from the national norm of 0.4

B) Assume that the study found that 32 of the 60 full-time students were employed and repeat (a). Are the conclusions the same?

Answer 1

Here we have to test that

Here

and

Conditions are satisfied.

A) Here x = number of full time students who are employed = 25

n = Total number of full time students at a university = 60

                        (Round to 4 decimal)

Test statistic:

z = 0.26                        (Round to 2 decimal)

Test statistic = 0.26

P value for two tailed test is

p value = 2 * P(z > 0.26)

            = 2 * (1 - P(z < 0.26))

           = 2 * (1 - 0.6026)

           = 2 * 0.3974

          = 0.7948

P value = 0.7948

Here p value = 0.7948 > alpha = 0.05

So we do not reject null hypothesis H0.

Conclusion: There is insufficient evidence to conclude that the proportion of full time students at the university is different from the national norm of 0.4.

B) Here x = number of full time students who are employed = 32

n = Total number of full time students at a university = 60

Test statistic:

z = 2.06                     (Round to 2 decimal)

P value for two tailed test is

p value = 2 * P(z > 2.06)

            = 2 * (1 - P(z < 2.06))

           = 2 * (1 - 0.9803)

           = 2 * 0.0197

          = 0.0394

P value = 0.0394

Here p value = 0.0394 < alpha = 0.05

So we reject null hypothesis H0.

Conclusion: There is sufficient evidence to conclude that the proportion of full time students at the university is different from the national norm of 0.4.

That means conclusions are not same.