The Family and Medical Leave Act provides job protection and unpaid time off for

Question

The Family and Medical Leave Act provides job protection and unpaid time off for full time employees in the U.S. from work for a serious illness or birth of a child. In 2000, 60% of the respondents of a survey stated that it was easy to get time off for these circumstances. A researcher wishes to see if the percentage who said it was easy to get time off has changed. A sample of 100 people who used the leave showed that 53% found it easy to get the leave.
a) In this study, define the following:
Population:
Sample:       Sample Size:
Sample Proportion:       Margin of Error:
b) Find the 95% confidence interval for the percent of people who found it easy to get the medical leave from the researcher’s sample. Interpret the 95% confidence interval in complete sentences written for a general audience.
c) The researcher would like to conduct a hypothesis test to evaluate his claim that the percent of people getting leave has changed. State the null and alternative hypotheses.
Null:
Alternative:
d) What is your decision regarding the null and alternative hypothesis? Explain your decision and write a conclusion using complete sentences for a general audience.

Explanation / Answer

a)
population - full time employees in the U.S.
sample -   100 people
sample size = 100

Sample Proportion: 0.53  
Margin of Error: z*sqrt(pq/n) = 1.96*sqrt(0.53*0.47/100)
= 0.097823

b) 95% confidence interval is
(0.432178, 0.627822)

c) Ho: p = 0.6
Ha: p not equal to 0.6

since 0.6 is present is confidence interval
we fail to reject it and conclude that there is not sufficient
evidence that percentage has changed

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