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?

Step-by-step explanation:

Analysis of the Data Given:

For sample 1 ,  the sample size

number of favorable cases

thus ; the sample proportion is

=

= 0.4195

For sample 2, the sample size

number of favorable cases

Then the sample proportion  is

=

= 0.2741

The value of the pooled proportion is computed as

=

= 0.3835

We are also given that the significance level is

Null Hypothesis : :  the proportion of workers that say monitoring employee e-mail is unethical is not greater than the proportion of bosses.

Alternative hypothesis : :  the proportion of workers that say monitoring employee e-mail is unethical is greater than the proportion of bosses.

:

:

The above corresponds to the right-tailed test , for which a z-test for the two population proportions needs to be conducted .

Rejection Region:

From the given information ; the significance level is

Then; the critical value for a right tailed test is

The rejection region for this right tailed test is R = {z : z > 2.33}

Test Statistics:

The z-statistic is computed as:

z = 3.014

Decision about the null hypothesis:

Since it is observed that z = 3.014 > ; it is concluded that the null hypothesis is rejected

Using the P-value approach: The P-value p = 0.0013 and since p = 0.0013<0.01 , it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the proportion of workers that say monitoring employee e-mail is unethical is greater than the proportion of  bosses.

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