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A survey of 410 workers showed that 172 said it was unethical to monitor employee e-mail. When 135 senior-level bosses were surveyed, 37 said it was unethical to monitor employee e-mail. At the 1% significance level, do the data provide sufficient evidence to conclude that the proportion of workers that say monitoring employee e-mail is unethical is greater than the proportion of bosses?

a. What is the Parameter of interest?
b. What is the underlying Distribution?

Respuesta :

Answer:

a)[tex]p_{w} -p_{b}[/tex]

With [tex]p_{w}[/tex] the proportion associated to the workers and [tex]p_{b}[/tex] the proportion for the bosses

b) [tex] \hat p_{w} -\hat p_{b} \sim N(p_w -p_b, \sqrt{\frac{p_w (1-p_w)}{n_w} +\frac{p_b (1-p_b)}{n_b} }[/tex]

With [tex]\hat p_w = 0.420, p_b = 0.274 , n_w = 410, n_b= 135[/tex]

Step-by-step explanation:

Part a

For this case we define the parameter of interest is the difference between the proportion of workers that say monitoring employee e-mail is unethical and the proportion of bosses that say monitoring employee e-mail is unethical

So the parameter can be expressed like this:

[tex]p_{w} -p_{b}[/tex]

With [tex]p_{w}[/tex] the proportion associated to the workers and [tex]p_{b}[/tex] the proportion for the bosses

Part b

For this case we want to find the distribution for [tex]p_{w} -p_{b}[/tex]

The estimated proportions for this case are:

[tex]\hat p_{w}= \frac{172}{410}= 0.420[/tex]

[tex]\hat p_{b}= \frac{37}{135}= 0.274[/tex]

We can assume that these estimators represnent unbiased estimators for the real parameter so then the distribution for the difference in the proportions can be assumed like this:

[tex] \hat p_{w} -\hat p_{b} \sim N(p_w -p_b, \sqrt{\frac{p_w (1-p_w)}{n_w} +\frac{p_b (1-p_b)}{n_b} }[/tex]

With [tex]\hat p_w = 0.420, p_b = 0.274 , n_w = 410, n_b= 135[/tex]

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