A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, and 36 square feet. (a) Figure the mean and standard deviation for the governors and for the CEOs. (b) Explain what you have done to a person who has never had a course in statistics. (c) Note the ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

I assume you can calculate the means and standard deviations.

In explaining the difference between means, you might mention the null hypothesis and alternate hypothesis (two-tailed or one-tailed), along with the probability of alpha (type I) error (rejecting null hypothesis when it is really true).

Whether you accept or reject the null hypothesis, then you need to interpret the meaning of your results.

Of course, you will need to elaborate this information. You will find that, if you can explain the process clearly to someone else, you will have a much clearer understanding of the process yourself. It makes your knowledge much more explicit. Good luck!

I hope this helps. Thanks for asking.

(a) To figure out the mean and standard deviation for both the governors and CEOs, we will need to calculate the average (mean) and the spread (standard deviation) of the given data.

For the governors:
Mean = (44 + 36 + 52 + 40) / 4 = 172 / 4 = 43 square feet

To calculate the standard deviation, follow these steps:
1. Find the difference between each data point and the mean: (44 - 43), (36 - 43), (52 - 43), and (40 - 43).
2. Square each difference: (44 - 43)^2, (36 - 43)^2, (52 - 43)^2, and (40 - 43)^2.
3. Find the average of these squared differences: [(44 - 43)^2 + (36 - 43)^2 + (52 - 43)^2 + (40 - 43)^2] / 4.
4. Take the square root of the result from step 3 to get the standard deviation for the governors.

For the CEOs:
Mean = (32 + 60 + 48 + 36) / 4 = 176 / 4 = 44 square feet

To calculate the standard deviation using the same steps as above.

(b) To someone unfamiliar with statistics, you can explain the process as follows:
- First, we are trying to find the average value of the square footage for the governors and CEOs. This is called the mean. To find the mean, we add up all the numbers and then divide the sum by the total number of values.
- Then, we want to understand how much the square footage values vary from the mean. This is called the standard deviation. It gives us an idea of how spread out the values are. We calculate the standard deviation by subtracting each value from the mean, squaring the differences, finding the average of those squared differences, and then taking the square root.

(c) Comparing the means and standard deviations of the governors and CEOs can provide insights into potential differences between these groups.
- Mean: The mean square footage for the governors is 43 square feet, while for the CEOs, it is 44 square feet. This suggests that, on average, the CEOs have slightly larger offices than the governors.
- Standard Deviation: The standard deviation measures the spread or variability of the data. If the standard deviation is high, it means that the data points are more spread out from the mean. In this case, without knowing the exact values, we can observe that the standard deviation of the CEOs might be larger than that of the governors. This implies that there is potentially more variation in the office sizes among the CEOs compared to the governors.

Speculating on the meaning of these differences, we could interpret them as follows:
- The slightly larger mean for CEOs may indicate that CEOs of major corporations tend to have larger office spaces compared to U.S. governors. This could be attributed to the nature of their roles and the resources available to corporations.
- The potentially larger standard deviation for CEOs suggests that there might be greater variability in the office sizes of CEOs compared to governors. This could be due to differences in company sizes, industries, or personal preferences of the CEOs.

It's important to note that these conclusions are based solely on the given data and might not be representative of all U.S. governors and large corporations' CEOs. Further research with a larger sample size would be needed for more generalizable conclusions.