Question

A sociologist sampled 200 people who work in computer-related jobs and found that 43 of them have changed jobs in the past 6 months. Can you conclude that more than 15% of computer-related workers have changed jobs in the past 6 months? Find the P-value and state a conclusion. The P-value is (Round the final answer to four decimal places.) We (Click to select) conclude that more than 15% of computer-related workers have changed jobs in the past 6 months.

Answer 1

Solution :

Given that,

= 0.15

Po

1 - = 0.85

Po

n = 200

x = 43

Level of significance = $\alpha$ = 0.05

Point estimate = sample proportion = $\hat p$ = x / n = 0.215

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.15

Ha: p 0.15

Test statistics

z = ($\hat p$ -
Po
) / $\sqrt{}$
Po
*(1-
Po
) / n

= ( 0.215 - 0.15) / $\sqrt{}$ (0.15*0.85) /200

= 2.574

P-value = P(Z > z )

= 1 - P(Z < 2.574 )

= 0.0050

Since, P-value = 0.0050 < 0.05, we reject the null hypothesis.

We reject the null hypothesis then conclude that more than 15% of computer- related workers have changed jobs in the past 6 months.