Respuesta :
Answer:
a) The point estimate of the proportion of people aged 65–69 who are working is p=0.3 or 30%.
b) We can express this null and alternative hypothesis as:
[tex]H_0: \pi=0.27\\H_1:\pi\neq0.27[/tex]
c) We conclude that there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
Step-by-step explanation:
a) Develop a point estimate of the proportion of people aged 65–69 who are working
If we take into account the sample taken, the point estimate is
[tex]p=\frac{180}{600} =0.3[/tex]
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
To conclude some claim, we have to reject the null hypothesis. In this case, to claim that the proportion has changed and the mean is no longer 27%, we have to reject the null hypotesis that π=0.27.
We can express this null and alternative hypothesis as:
[tex]H_0: \pi=0.27\\H_1:\pi\neq0.27[/tex]
c) Conduct your hypothesis test using α=0.05. What is your conclusion?
First we calculate the standard deviation, as we will need it to calculate the test statistic:
[tex]\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.27(1-0.27)}{600} }=0.01812[/tex]
In this case, we have a test statistic of
[tex]z=\frac{p-\pi-0.5/N}{\sigma} =\frac{0.3-0.27-0.5/600}{0.01812}=1.61[/tex]
If we take into account that it is a two-tailed test, P-value for z=1.61 is P=0.1074.
As the P-value is bigger than the significance level, the effect is not statistically significant, so the hypothesis can not be rejected.
We conclude that there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
A point estimate of the proportion of people aged 65–69 who are working is p=0.3 or 30%, 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 is H_0: π =0.27 and H_1: π not equal to -0.27. My hypothesis test using α 5 .05 is that there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
Explanation:
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
a. Develop a point estimate of the proportion of people aged 65–69 who are working. By taking into account the sample that taken, the point estimate is [tex]p=\frac{180}{600} =0.3[/tex]
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.
In this case to claim that the proportion has changed and the mean is no longer 27%, we have to reject the null hypotesis (π=0.27). The null and alternative hypothesis are:
[tex]H_0: \pi = 0.27\\ H_1 : \pi \neq 0.27[/tex]
c. Conduct your hypothesis test using α 5 .05. What is your conclusion?
Calculating the test statistic:
[tex]\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.27(1-0.27)}{600} } = 0.01812[/tex]
The test statistic
[tex]z=\frac{p-\pi-0.5/N}{\sigma} =\frac{0.3-0.27-0.5/600}{0.01812}=1.61[/tex]
It is a two-tailed test, P-value for z=1.61 is P=0.1074.
The hypothesis can not be rejected because as the P-value is bigger than the significance level, the effect is not statistically significant
Therefore there is not enough evidence that the proportion of people aged 65–69 who are working has increased from 2005.
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