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In recent years more people have been working past the age of 65. In 2005, 27%...

In recent years more people have been working past the age of 65. In 2005, 27% of people aged 65–69 worked. A recent report from the Organization for Economic Co-operation and Development (OECD) claimed that the percentage working had increased (USA Today, November 16, 2012). The findings reported by the OECD were consistent with taking a sample of 600 people aged 65-69 and finding that 180 of them were working.

a. Develop a point estimate of the proportion of people aged 65-69 who are working (to 2 decimals).

b. Set up a hypothesis test so that the rejection of H0 will allow you to conclude that the proportion of people aged 65-69 working has increased from 2005.
H0: p - Select your answer -greater than or equal to .27greater than .27less than or equal to .27less than .27equal to .27not equal to .27Item 2
Ha: p - Select your answer -greater than or equal to .27greater than .27less than or equal to .27less than .27equal to .27not equal to .27Item 3

c. Conduct your hypothesis test using α=.05.

p-value - Select your answer -greater than or equal to .05, rejectgreater than .05, do not rejectless than or equal to .05, rejectless than .05, do not rejectequal to .05, rejectnot equal to .05, rejectItem 4

What is your conclusion?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(a) Point estimate of proportion of people aged 65 - 69 who areworking = p = 180/600 = 0.3

(b) H0: p 0.27

Ha: p > 0.27

(c)

p = 0.27

q = 1- p = 0.73

n = 600

SE =

Test statistic is:

Z = (0.3 - 0.27)/0.0181 = 1.6575

= 0.05

OneTail - Right Side Test

From Table,critical value of Z= 1.645

Since the calculated value of Z = 1.6575 is greater than critical value of Z= 1.645, difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the proportion of people aged 65 - 69 working has increased from 2005.

Correct option:

p-value 0.05, reject.

Table of Area Under Standard Normal Curve gives area = 0.4515

So,

p-value= 0.5 - 0.4515 = 0.0485

So,

Conclusion: Reject null hypothesis

The data support the claim that the proportion of people aged 65 - 69 working has increased from 2005.

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