Question

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 77 students shows that 37 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance. What are we testing in this problem?

Answer 1

Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs, is statistically evident.

Explanation:

Here we are testing whether proportion of the students at Flora College who work while attending school is 35% or more than 35%

`H_0: p = 0.35\\H_a: p >0.35`

(Right tailed test at 5% level of significance)

Sample proportion p =
`(37)/(77) \\=0.4805`

Assuming H0 to be true, std error of proportion =
`√(0.35*0.65/77) \\=0.0544`

p difference = 0.1305

Z = test statistic = 2.40

p value for one tailed = 0.0082

Since p < 0.05 we reject H0

Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs, is statistically evident.