MATH SOLVE

4 months ago

Q:
# 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 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.b. Set up a hypothesis test so that the rejection of h0 will allow you to conclude that theproportion of people aged 65–69 working has increased from 2005.c. Conduct your hypothesis test using α 5 .05. What is your conclusion?

Accepted Solution

A:

Answer:a) point estimate is 30%b) null and alternative hypothesis would be[tex]H_{0}[/tex]: p=27%[tex]H_{a}[/tex]: p>27%c) We reject the null hypothesis, percentage working people aged 65-69 had increased Step-by-step explanation:a. Point estimate would be the proportion of the working people aged 65–69 to the sample size and equals [tex]\frac{180}{600}=0.3[/tex] ie 30%b.Let p be the proportion of people aged 65–69 who is working. OECD claims that percentage working had increased. Then null and alternative hypothesis would be[tex]H_{0}[/tex]: p=27%[tex]H_{a}[/tex]: p>27%c.z-score of the sample proportion assuming null hypothesis is:[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where p(s) is the sample proportion of working people aged 65–69 (0.3)p is the proportion assumed under null hypothesis. (0.27)N is the sample size (600)then z=[tex]\frac{0.3-0.27}{\sqrt{\frac{0.27*0.73}{600} } }[/tex] = 1.655Since one tailed p value of 1.655 = 0.048 < 0.05, sample proportion is significantly different than the proportion assumed in null hypothesis. Therefore we reject the null hypothesis.