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Many employers are concerned about employees wasting time by surfing the Internet and e-mailing friends during work hours. The article "Who Goofs Off 2 Hours a Day? Most Workers, Survey Says" summarized data from a large sample of workers.† Suppose that the CEO of a large company wants to determine whether the mean wasted time during an $8$-hour workday for employees of her company is less than the mean of $120$ minutes reported in the article. Each person in a random sample of $10$ employees is asked about daily wasted time at work (in minutes). Participants would be guaranteed anonymity to obtain truthful responses. Suppose the resulting data are as follows.

$$132, 80, 140, 97, 91, 120, 103, 149, 115, 87$$

Question states: Calculate the point estimate (in minutes) for the population mean.

The solution is: $111.4$

My question is why is it simply the average of those numbers from the second sample. I thought the idea of point estimates was to take the first mean and subtract off the second mean such as $\bar{x}_1 - \bar{x}_2$, or for populations $\mu_1 - \mu_2$. Why is the point estimate in this case just the average of the cases from the sample?


Will surely up-vote best answer

Thank you

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  • $\begingroup$ I don't understand your question. Where is the "second sample"? $\endgroup$ – mzp Apr 4 '18 at 0:11
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There is no second sample here (or no first sample, I guess since you seem to be thinking of the 10 data points you have as "the second sample"). You have a single sample from your company and are trying to make an inference about the mean time wasted for employees in your company (the population).

In particular, you are trying to see if it's greater than or less than 120 minutes.

This business with $\bar x_1-\bar x_2$ is for when you have two samples, from two different populations, and are trying to make an inference about how the population means compare. In fact, this question does sort of fit into that framework since you have it on good authority that the $120$ minutes is the mean time wasted across all companies, which you can think of as another population. However, we are assuming we know the mean of this larger population exactly (i.e. it is 120 minutes), and not getting information about it from a sample.

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