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The sample mean is a way to measure the central tendency of your data. It's like finding the average of your dataset. You simply add up all the data points and divide by the number of data points you have.
In the given exercise, the times spent on non-job-related activities are added: 7, 1, 29, 8, 1, 14, 1, 41, and 6. That's a total of 108.
Since there are 9 employees, you divide 108 by 9. The sample mean \(\bar{x}\) is 12.
The sample mean helps us understand the average behavior of the group being studied. In this exercise, it tells us the average time spent on non-job-related activities per employee.

Standard deviation is a way to measure how spread out your data is. When data points are close to the mean, the standard deviation is small. When they are spread out, it's large.
To find the standard deviation, follow these steps:

• Subtract the sample mean from each data point.
• Square each result to eliminate negative values.
• Add all the squared results together.
• Divide by the number of data points minus one (this gives you the variance).
• Take the square root of the variance to find the standard deviation.

This measure tells us how much variation there is from the sample mean. In the context of the exercise, it indicates how consistent employees' non-job-related computer use is.

The Z-value is a statistical measure that tells us how many standard deviations away an element is from the mean. It's crucial for creating confidence intervals.
For a 95% confidence interval, which is common in statistical problems, the Z-value from the standard normal distribution is typically 1.96. This value is based on the assumption that the population from which you are sampling is normally distributed.
Note that before using a Z-value, it's essential to ensure your sample size is large enough or that the population is already assumed to be normally distributed, as stated in the original exercise.
This Z-value is used later, alongside the standard deviation and sample size, to calculate the margin of error.

The margin of error represents the range within which we expect the true population mean to lie. It quantifies the uncertainty or possible error in our sample estimate.
To calculate it, multiply the Z-value by the standard deviation divided by the square root of the sample size: \(E = z* \cdot \frac{s}{\sqrt{n}}\).
For the exercise, this calculation gives us a buffer around the sample mean to account for sampling variability.
The confidence interval itself is then the sample mean plus or minus this margin of error. It provides a range where the true average time spent on non-job-related activities is likely located, considering the sample data.