Question

From previous studies, it is concluded that 80% of workers indicate that they are dissatisfied with their job. A researcher claims that the proportion is larger than 80% and decides to survey 200 working adults. Test the researcher's claim at the α=0.005 significance level.

1) Verify np(1−p)≥10. Round your answer to one decimal place.

np(1−p) =

2) Based on the sample of 200 people, 89% workers indicate that they are dissatisfied with their job. What is the test statistic? Round your answer to two decimal places.

= ?

3) What is the p-value? Round your answer to four decimal places.

Answer 1

Here, n = 200 and p = 80% = 0.8

1)np(1-p) = 200*0.8*0.2

= 32 , which is greater than 10.

Therefore, it is verified.

2) A researcher claims that the proportion of workers dissatisfied with their job is larger than 80%. To test :

H0 : p = 0.80

H1 : p > 0.80

The sample proportion, = 0.89 and n = 200

The test statistic , z = ( - p) / p(1-p)/n

= 0.09 / 0.0282

= 3.19

The test statistic is z = 3.19.

3) We find the p-value for this corresponding test statistic using MS-Excel. Using MS-Excel, the p value is :

p = 0.0007

Since p-value is less than the significance level we reject the null hypothesis at level 0.005 and conclude that the proportion of workers dissatisfied with their job is larger than 80%.