Question

QUESTION 10

1. Question 10-12 are based on the following:

   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.

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

0.075 points   

QUESTION 11

1. 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 less than 0.27    Ha: p equal to 0.27
   		H0: p less than or equal to 0.27    Ha: p greater than 0.27
   		H0: p greater than or equal to 0.27    Ha: p less than 0.27
   		H0: p equal to 0.27    Ha: p greater than 0.27

0.075 points   

QUESTION 12

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

   p-value _____________

   Do we reject? ___________

   What is your conclusion? ______________

   		greater than or equal to 0.05; Reject; Conclude that the proportion of people aged 65-69 has not increased since 2007.
   		less than or equal to 0.05; Reject; Conclude that the proportion of people aged 65-69 has increased since 2007.
   		equal to 0.05; Do not reject; Conclude that the proportion of people aged 65-69 has increased since 2007.
   		less than or equal to 0.05; Do not reject; Conclude that the proportion of people aged 65-69 has not increased since 2007.

Answer 1

Solution :

10 and11)

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.27

H_a : p > 0.27

n = 600

x = 180

= x / n = 180 / 600 = 0.3

P₀ = 0.27

1 - P₀ = 1 - 0.27 = 0.73

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3 - 0.27 / [(0.27 * 0.73) / 600]

= 1.655

Test statistic = 1.655

12)

P(z > 1.655) = 1 - P(z < 1.655) = 1 - 0.951 = 0.049

P-value = 0.049

= 0.05

P-value <

Reject the null hypothesis .

Less than or equal to 0.05; Reject; Conclude that the proportion of people aged 65-69 has increased since 2007.