Question

13.) According to a recent​ report, 46​% of college student internships are unpaid. A recent survey of 120 college interns at a local university found that 60 had unpaid internships.

- Use the​ five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of college interns that had unpaid internships is different from 0.46. Assume that the study found that 69 of the 120 college interns had unpaid internships and repeat​ (a). Are the conclusions the​ same?

Let π be the population proportion. Determine the null​ hypothesis, H0​, and the alternative​ hypothesis,

H1​: π = ____

H1​: π ≠ ____

​(Type integers or decimals. Do not​ round.)

- What is the test​ statistic? ZSTAT = _____ ​ (Round to two decimal places as​ needed.)

- What is the​ p-value? ​(Round to three decimal places as​ needed.)

- What is the final​ conclusion?   ________ the null hypothesis. There _____ sufficient evidence that the proportion of college interns that had unpaid internships is ________ 0.46 because the​ p-value is ________ the level of significance.

- Assume that the study found that 60 of the 120 college interns had unpaid internships and repeat​ (a). What is the test​ statistic? ZSTAT = _____ ​(Round to two decimal places as​ needed.)

- What is the​ p-value? The​ p-value is _____ (Round to three decimal places as​ needed.)

- What is the final​ conclusion? The result is ___________ part​ (a). ________ the null hypothesis. There ____ sufficient evidence that the proportion of college interns that had unpaid internships _____________ 0.46 because the​ p-value ____________ the level of significance.

14.) Recently, a large academic medical center determined that 9 of 23 employees in a particular position were male​, whereas 57% of the employees for this position in the general workforce were male. At the 0.01 level of​ significance, is there evidence that the proportion of male in this position at this medical center is different from what would be expected in the general​ workforce?

What are the correct hypotheses to test to determine if the proportion is​ different?

- Calculate the test statistic. ZSTAT = _______

- What is the​ p-value? The​ p-value is ________

- State the conclusion of the test. __________ the null hypothesis. There is __________ evidence to conclude that the proportion of male in this position at this medical center is different from the proportion in the general workforce.

Answer 1

13 )

a) Given : n=120 , x=69

Therefore , the sample proportion , p=x/n=69/120=0.58

Hypothesis : Vs

The test statistic is ,

The P-value is ,

P-value =

Decision Rule : Here , P-value = 0.0041 < =0.05

Therefore , reject Ho at =0.05 significance level.

Conclusion : There is sufficient evidence that the proportion of college interns that had unpaid internships is different from 0.46 because the P-value is less than the level of significance.

b) Given : n=120 , x=60

Therefore , the sample proportion , p=x/n=60/120=0.50

Hypothesis : Vs

The test statistic is ,

The P-value is ,

P-value =

Decision Rule : Here , P-value = 0.1894> =0.05

Therefore , fail to reject Ho at =0.05 significance level.

Conclusion : There is not sufficient evidence that the proportion of college interns that had unpaid internships is different from 0.46 because the P-value is greater than the level of significance.

14)

Given : n=23 , x=9

Therefore , the sample proportion , p=x/n=9/23=0.39

Hypothesis : Vs

The test statistic is ,

The P-value is ,

P-value =

Decision Rule : Here , P-value = 0.0409 > =0.01

Therefore , fail to reject Ho at =0.01 significance level.

Conclusion : There is not sufficient evidence that the proportion of male in this position at this medical center is different from the proportion in the general workforce.