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 85 students shows that 38 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

What is the level of significance?

State the null and alternate hypotheses.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

Find the P-value. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

= 0.35

1 - = 0.65

n = 85

x = 38

Point estimate = sample proportion = = x / n = 0.447

Level of significance = = 0.05

This a right (One) tailed test.

Ho: p = 0.35

Ha: p 0.35

Test statistics

z = ( - ) / *(1-) / n

= ( 0.447 - 0.35) / (0.35*0.65) /85

= 1.875

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 1.875)

= 1 - 0.9696

= 0.0304

The p-value is p = 0.0304, and since p = 0.0304 < 0.05, it is concluded that the null hypothesis is rejected.