Water scarcity has traditionally been a major concern in the Canary Islands. Water rights are divided into shares, which are privately owned. The article “The Social Construction of Scarcity. The Case of Water in Tenerife (Canary Islands)” discusses the extent to which many of the shares are concentrated among a few owners. The following table presents the number of owners who own various numbers of shares. (There were 15 owners who owned 50 shares or more; these are omitted.) Note that it is possible to own a fractional number of shares; for example, the interval 2–< 3 contains 112 individuals who owned at least 2 but less than 3 shares.

$$\begin{matrix} \text{Number of Shares} & \text{Number of Owners}\\ \text{0–< 1} & \text{18}\\ \text{1–< 2} & \text{165}\\ \text{2–< 3} & \text{112}\\ \text{3–< 4} & \text{87}\\ \text{4–< 5} & \text{43}\\ \text{5–< 10} & \text{117}\\ \text{10–< 15} & \text{51}\\ \text{15–< 20} & \text{32}\\ \text{20–< 25} & \text{10}\\ \text{25–< 30} & \text{8}\\ \text{30–< 50} & \text{8}\\ \end{matrix}$$

a. Construct a histogram for these data. b. Approximate the median number of shares owned by finding the point for which the areas on either side are equal. c. Approximate the first quartile of the number of shares owned by finding the point for which 25% of the area is to the left. d. Approximate the third quartile of the number of shares owned by finding the point for which 75% of the area is to the left.

A commuter encounters four traffic lights each day on her way to work. Let X represent the number of these that are red lights. The probability mass function of X is as follows.

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4}\\ \text{P(X = x)} & \text{0.1} & \text{0.3} & \text{0.3} & \text{0.2} & \text{0.1}\\ \end{matrix}$$

What is the probability that in a period of 100 days, the average number of red lights encountered is more than 2 per day?

In the Statistics Norway on-line article “The Times They Are a Changing,” J. Kristiansen discussed the changes in age at the time of marriage in Norway. The ages, in years, at the time of marriage for 75 Norwegian couples are presented on the WeissStats CD. Use the technology of your choice to do the following. a. Decide, at the 1% significance level, whether the data provide sufficient evidence to conclude that the mean age of Norwegian men at the time of marriage exceeds that of Norwegian women. b. Find and interpret a 99% confidence interval for the difference between the mean ages at the time of marriage for Norwegian men and women. c. Remove the two paired-difference (potential) outliers and repeat parts (a) and (b). Compare your results to those in parts (a) and (b).

The fill volume of cans filled by a certain machine is normally distributed with mean 12.05 oz and standard deviation 0.03 oz. a. What proportion of cans contain less than 12 oz? b. The process mean can be adjusted through calibration. To what value should the mean be set so that 99% of the cans will contain 12 oz or more? c. If the process mean remains at 12.05 oz, what must the standard deviation be so that 99% of the cans will contain 12 oz or more?

Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed to examine factors that determine social status for children in grades 4, 5, and 6. Researchers gave a questionnaire to a random sample of 478 students in these grades. One of the questions they asked was, "What would you most like to do at school: Make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses.

$$\begin{array} {lc} & \text{Gender} \\ \text {Goal} & \begin{array}{l|c|c|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text { Grades } & 130 & 117 & 247 \\ \hline \text { Popular } & 91 & 50 & 141 \\ \hline \text { Sports } & 30 & 60 & 90 \\ \hline \text { Total } & 251 & 227 & 478 \end{array}\\ \end{array}$$

Construct an appropriate graph to compare male and female responses. Briefly describe the relationship between gender and goals for these students.

A variable has a mean of 100 and a standard deviation of 16. Four observations of this variable have a mean of 108 and a sample standard deviation of 12. Determine the observed value of the a. standardized version of $\bar{x}$. b. studentized version of $\bar{x}$.

In the article “Occurrence and Distribution of Ammonium in Iowa Groundwater” ammonium concentrations (in mg/L) were measured at a total of 349 alluvial wells in the state of Iowa. The mean concentration was 0.27, the median was 0.10, and the standard deviation was 0.40. If a histogram of these 349 measurements were drawn, i. it would be skewed to the right. ii. it would be skewed to the left. iii. it would be approximately symmetric. iv. its shape could not be determined without knowing the relative frequencies.

a. find the regression equation for the data points. b. graph the regression equation and the data points.

$$\begin{array}{l|lll} \hline x & 2 & 4 & 3 \\ \hline y & 3 & 5 & 7 \\ \hline \end{array}$$

In the article "Fossil Argonauts (Mollusca: Cephalopoda: Octopodida) from Late Miocene Siltstones of the Los Angelas Basin, California", paleontologists L. Saul and C. Stadum discussed fossilized Argonaut egg cases from the late Miocene period found in California. A sample of 10 fossilized egg cases yielded the following data on height, in millimeters. Obtain the mean, median, and mode(s) of these data.

$$\begin{array}{lllll} \hline 37.5 & 31.5 & 27.4 & 21.0 & 32.0 \\ 33.0 & 33.0 & 38.0 & 17.4 & 34.5 \\ \hline \end{array}$$

Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing. Do you think increasing incomes cause decreasing times to run the mile? Explain.

Evaluate each expression without using a calculator $\left[\left(\frac{2}{3}\right)^{-2}\right]^{-1}$

Evaluate each expression. If $f(x)=\frac{3}{x^{4}},$ find $f^{\prime \prime}(-1)$.

Consider the standardized variable $z=\frac{b_{1}-\beta_{1}}{\sigma / \sqrt{S_{x x}}}$. a. Identify its distribution. b. Why can’t it be used as the test statistic for a hypothesis test concerning $\beta_{1}$? c. What statistic is used? What is the distribution of that statistic?

Every random sample of the same size from a given population will produce exactly the same confidence interval for $\mu$. Answer true or false. Explain your answer.