The 92 million Americans of age 50 and over control 50% of all discretionary income (AARP Bulletin, March 2008). AARP estimated that the average annual expenditure on restaurants and carry out food was $1873 for individuals in this age group. Suppose this estimate is based on a sample of 80 persons and that the sample standard deviation is $550.

c. What is your estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food?
d. If the amount spent on restaurants and carryout food is skewed to the right, would you expect the median amount spent to be greater or less than $1873?

c. To estimate the total amount spent by Americans of age 50 and over on restaurants and carryout food, you can use the formula:

Total estimate = Sample estimate * Population size

Given that the sample estimate is $1873, the population size is 92 million, and the sample size is 80, you can calculate the estimate as follows:

Total estimate = $1873 * (92,000,000 / 80)

Total estimate = $1873 * 1,150,000

Total estimate ≈ $2,154,950,000

Therefore, your estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food is approximately $2,154,950,000.

d. If the amount spent on restaurants and carryout food is skewed to the right, it means that there are some extreme high values or outliers that pull the distribution towards the right side. In such a case, the median amount spent would be less than the mean ($1873).

This is because the median is less affected by extreme values compared to the mean. It represents the middle value when the data is arranged in ascending order. If there are some unusually high values, they would have more impact on the mean, but the median would be less affected.

Therefore, if the amount spent on restaurants and carryout food is skewed to the right, you would expect the median amount spent to be less than $1873.

To estimate the total amount spent by Americans of age 50 and over on restaurants and carryout food, you can multiply the average annual expenditure per person by the total number of Americans in that age group.

c. To calculate the estimate, use the formula:
Total amount spent = (Average annual expenditure per person) x (Total number of Americans in that age group)

Average annual expenditure per person = $1873 (given in the question)
Total number of Americans in that age group = 92 million (given in the question)

Total amount spent = $1873 x 92 million

Therefore, your estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food would be $1873 multiplied by 92 million.

d. If the amount spent on restaurants and carryout food is skewed to the right, it means that there are a few individuals who spend significantly more than the average. In such cases, the median, which represents the middle value when the data is ordered, is expected to be greater than the mean (average) amount spent. This is because a few individuals with high spending can pull the average up, but they may not necessarily affect the median. So, in this case, you would expect the median amount spent to be greater than $1873.

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