Find out the margin of error and the $95 \%$ confidence interval for the following study. Briefly interpret the $95 \%$ confidence interval. A $2016$ survey of $2010$ adults by the Pew Research Center found that $83 \%$ of those surveyed support background checks for private and gun show sales.

Find out the margin of error and the $95 \%$ confidence interval for the following study. Briefly interpret the $95 \%$ confidence interval. A $2017$ Gallup poll of $1035$ adults found that $37 \%$ of those surveyed believe the United Nations is doing a good job solving global problems.

Find out the margin of error and the $95 \%$ confidence interval for the following study. Briefly interpret the $95 \%$ confidence interval. A recent survey of $65,000$ households by the U.S. Department of Labor reported an unemployment rate of $4.3 \%$.

The following table shows binned data for the percentages of high school graduates who took the ACT test in $2016$ among the $50$ states and the District of Columbia. Make a histogram of the data.

$$\begin{aligned} &\text { ACT Test Takers by State }\\ &\begin{array}{c|c} \hline \begin{array}{c} \text { Percentage of } \\ \text { high school graduates } \end{array} & \text { Number of states } \\ \hline \leq 20 \% & 2 \\ 21-40 \% & 14 \\ 41-60 \% & 6 \\ 61-80 \% & 6 \\ 81-100 \% & 23 \end{array} \end{aligned}$$

Assume that you want to decrease the margin of error by a factor of $10$ -for example, from $1 \%$ to $0.1 \%$. By what factor must you increase the sample size? Explain.

You are trying to identify the cause of late-afternoon headaches that plague you several days each week. For each of the following tests and observations, explain which of the six guidelines for establishing causality you used and what you concluded.

• The headaches occur only on days when you go to work.
• If you stop drinking Coke at lunch on days when you go to work, the headaches persist.
• In the summer, the headaches occur less frequently if you open the windows of your office slightly. They occur even less often if you open the windows of your office fully. Having made all these observations, what reasonable conclusion can you reach about the cause of the headaches?

Total revenue is in dollars and $x$ is the number of units.

Suppose that in a monopoly market, the demand function for a product is given by

$$p=160-0.1 x$$

where $x$ is the number of units and $p$ is the price in dollars.

(a) Find the total revenue from the sale of $500$ units.

(b) Find and interpret the marginal revenue at $500$ units.

( c ) Is more revenue expected from the $501$ st unit sold or from the $701$st? Explain.

Find $\frac{d C}{d x}$ for $C=\frac{5 x^4-2 x^2+1}{x^3+1}$.

Find out an example of a graph of geographical data in a recent news report. Comment on the effectiveness of the display. Could another type of graphic have been used to depict the same data?

Decide whether the following statement is a true or false sense. Explain your reasoning. I examined the data carefully, and the range was greater than the standard deviation.

Visit the websites of polling organizations, and gather the results of a particular poll. Describe the details of the actual polling procedure. Interpret the results in terms of a $95 \%$ confidence interval. What conclusions can you draw? Explain.

Complete the table.

An auto transmission manufacturer receives ball bearings from two different suppliers. The ball bearings must have a specified diameter of $16.30$ millimeters (mm) with a tolerance of $\pm 0.1 \mathrm{~mm}$. Recent shipments from the two suppliers had ball bearings with the following diameters.

Supplier A: $16.25,16.27,16.29,16.31,16.34,16.37,16.41$ Supplier B: $16.19,16.22,16.28,16.34,16.39,16.42,16.44$ a. Find out the mean and standard deviation of each data set. b. Draw a boxplot for each data set, and mark the tolerance on each boxplot. c. What percentage of ball bearings from each supplier meet the specifications?

The following table gives the average (median) weekly incomes of American workers (men and women) in several age categories. a. Choose an appropriate graph to display these data. Then write a short paragraph explaining any noticeable trends or patterns. b. For each age category, compute the gender wage gap: the ratio of the women's to men's earnings. Then write a short paragraph explaining any noticeable patterns.