# mathematics

1. How much time do Americans spend eating or drinking? Suppose for a random sample of 1001 Americans age 15 or older, the mean amount of time spent eating or drinking per day is 1.22 hours with a standard deviation of .65 hour.

A) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.

C) Determine and interpret a 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.
D) Could the interval be used to estimate the mean amount of time a 9-year-old American spends eating and drinking each day? Explain.
2) A researcher wanted to determine the mean number of hours per week(Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey indicate that s=7.5 hours
A) How many people are needed to estimate the number of hours people watch television per week within 2 hours with 95% confidence?

QUESTION 1:

A firm has three investment alternatives, as indicated in the following payoff table (payoffs in thousands of dollars):

See attachment…

To understand this table, let’s look at the first investment possibility, a (designated decision 1, or d1). First of all, there are three possible scenarios: s1, economic conditions improve; s2, conditions remain stable; s3, the economy nosedives. The respective probabilities for each scenario are 0.4, 0.3, and 0.3. Under d1, if the economy improves, the payoff will be 100K; if stable, 25K, if the economy is poor, the payoff is 0.

The second investment strategy is somewhat less sensitive to economic conditions, and the third is not influenced by the economy at all, guaranteeing a 50K payoff.

Using the expected value approach, which decision is preferred?

QUESTION 2:

Once again referring to the payoff table that appeared in LST 4-1 (payoffs in thousands of dollars):

a. For the lottery having payoffs of \$100K with probability p and \$0 with probability (1-p), two decision makers expressed the indifference probabilities in the table below.

Find the most preferred decision for each decision maker using the expected utility approach (to do this: for each decision maker, substitute their indifference probabilities multiplied by ten — which arbitrarily corresponds to an indifference probability of 1.0 — for the corresponding actual values in the payoff table. Then compute the expected utility for each alternative, using these new values and the actual probabilities, exactly as you would compute expected values with actual payoffs)

b. Why don’t A and B select the same decision alternative? (that is, how do their decisions reflect their respective attitudes to risk?)

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