Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the $95 \%$ and $99 \%$ confidence intervals for the mean:

$$\begin{array}{llllllllll}66 & 34 & 59 & 56 & 51 & 45 & 38 & 58 & 52 & 52 \\ 50 & 34 & 42 & 61 & 53 & 48 & 57 & 47 & 50 & 54\end{array}$$

A simple random sample of 25 has been collected from a normally distributed population for which it is known that $\sigma=17.0$. The sample mean has been calculated as $342.0$, and the sample standard deviation is $s=14.9$. Construct and interpret the $95 \%$ and $99 \%$ confidence intervals for the population mean.

According to Nielsen/NetRatings, the average visitor to amazon.com spends $19.7$ minutes at the site. Assuming this finding to be based on a simple random sample of 20 visitors to the site, with a sample standard deviation of $s=4.0$ minutes, and from a population that is approximately normally distributed, construct and interpret the $98 \%$ confidence interval for the population mean. Given this confidence interval, would it seem very unusual if another sample of this size were to have a mean visiting time of $18.5$ minutes?

A college student has two options for meals: eating at the dining hall for $\$ 6$ per meal, or eating a Cup O'Soup for $\$ 1.50$ per meal. His weekly food budget is $\$ 60$.

Suppose the price of a Cup O'Soup now rises to $\$ 2$. Using your diagram from part (a), show the consequences of this change in price. Assume that our student now spends only $30$ percent of his income on dining hall meals. Label the new optimum as point $B$.

A college student has two options for meals: eating at the dining hall for $\$ 6$ per meal, or eating a Cup O'Soup for $\$ 1.50$ per meal. His weekly food budget is $\$ 60$.

What happened to the quantity of Cups O'Soup consumed as a result of this price change? What does this result say about the income and substitution effects? Explain.

A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O’ Soup for$1.50 per meal. His weekly food budget is $60.

What happened to the quantity of Cups O’ Soup consumed as a result of this price change? What does this result say about the income and substitution effects? Explain.

A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O’ Soup for$1.50 per meal. His weekly food budget is $60.

Suppose the price of a Cup O’ Soup now rises to$2. Using your diagram from the previous part, show the consequences of this change in price. Assume that our student now spends only 30 percent of his income on dining hall meals. Label the new optimum as point B.

A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O’ Soup for$1.50 per meal. His weekly food budget is $60.

Draw the budget constraint showing the trade-off between dining hall meals and Cups O’ Soup. Assuming that he spends equal amounts on both goods, draw an indifference curve showing the optimum choice. Label the optimum as point A.

A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O’ Soup for$1.50 per meal. His weekly food budget is $60.

Use points A and B to draw a demand curve for Cup O’ Soup. What is this type of good called?

A college student has two options for meals: eating at the dining hall for $\$ 6$ per meal, or eating a Cup O'Soup for $\$ 1.50$ per meal. His weekly food budget is $\$ 60$.

Use points $A$ and $B$ to draw a demand curve for Cup O' Soup. What is this type of good called?

Darius buys only milk and cookies.

a. In year $1$ , Darius earns $\$ 100$, milk costs $\$ 2$ per quart, and cookies cost $\$ 4$ per dozen. Draw Darius's budget constraint.

b. Now suppose that all prices increase by $10$ percent in year $2$ and that Darius's salary increases by $10$ percent as well. Draw Darius's new budget constraint. How would Darius's optimal combination of milk and cookies in year $2$ compare to his optimal combination in year $1$ ?

You consume only soda and pizza. One day, the price of soda goes up, the price of pizza goes down, and you are just as happy as you were before the price changes.

Can you afford the bundle of soda and pizza you consumed before the price changes?

You consume only soda and pizza. One day, the price of soda goes up, the price of pizza goes down, and you are just as happy as you were before the price changes.

How does your consumption of the two goods change? How does your response depend on income and substitution effects?

You consume only soda and pizza. One day, the price of soda goes up, the price of pizza goes down, and you are just as happy as you were before the price changes. a. Illustrate this situation on a graph. b. How does your consumption of the two goods change? How does your response depend on in come and substitution effects? c. Can you afford the bundle of soda and pizza you consumed before the price changes?