Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams per liter, or mg/l) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the table.

$$\begin{array}{|l|c|c|c|c|c|} \hline \text { Well } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Bottom } & 0.430 & 0.266 & 0.567 & 0.531 & 0.707 \\ \hline \text { Top } & 0.415 & 0.238 & 0.390 & 0.410 & 0.605 \\ \hline \text { Well } & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Bottom } & 0.716 & 0.651 & 0.589 & 0.469 & 0.723 \\ \hline \text { Top } & 0.609 & 0.632 & 0.523 & 0.411 & 0.612 \\ \hline \end{array}$$

Make a dotplot of the differences (Bottom - Top) in the zinc concentrations for these 10 wells. What does the graph reveal?

A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that's 40 ounces ) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.

Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams per liter, or mg/l) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the table.

$$\begin{array}{|l|c|c|c|c|c|} \hline \text { Well } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Bottom } & 0.430 & 0.266 & 0.567 & 0.531 & 0.707 \\ \hline \text { Top } & 0.415 & 0.238 & 0.390 & 0.410 & 0.605 \\ \hline \text { Well } & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Bottom } & 0.716 & 0.651 & 0.589 & 0.469 & 0.723 \\ \hline \text { Top } & 0.609 & 0.632 & 0.523 & 0.411 & 0.612 \\ \hline \end{array}$$

Construct and interpret a 95% confidence interval for the true mean difference in the zinc concentrations at the top and bottom of the wells in this region.

Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams per liter, or mg/ l ) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the table.

$$\begin{array}{|l|c|c|c|c|c|} \hline \text{Well} & 1 & 2 & 3 & 4 & 5 \\ \hline \text{Bottom} & 0.430 & 0.266 & 0.567 & 0.531 & 0.707 \\ \hline \text{Top} & 0.415 & 0.238 & 0.390 & 0.410 & 0.605 \\ \hline \text{Well} & 6 & 7 & 8 & 9 & 10 \\ \hline \text{Bottom} & 0.716 & 0.651 & 0.589 & 0.469 & 0.723 \\ \hline \text{Top} & 0.609 & 0.632 & 0.523 & 0.411 & 0.612 \\ \hline \end{array}$$

Does your interval in the previous part give convincing evidence of a difference in the average zinc concentrations between the top and bottom of wells in this region? Justify your answer.

Emirates Airline offers one outbound flight from Dubai, United Arab Emirates, to Doha, Qatar, and one return flight from Doha to Dubai each day. An experienced Emirates pilot suspects that the Dubai-to-Doha outbound flight typically takes longer. To find out, the pilot collects data about these flights on a random sample of 12 days. The table displays the flight times in minutes.

$$\begin{array}{lcccccccccccc} \hline \text { Day } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \begin{array}{l} \text { Outbound } \\ \text { (Dubal } \rightarrow \text { Doha) } \\ \text { Return } \end{array} & 75 & 42 & 62 & 63 & 54 & 46 & 52 & 50 & 42 & 46 & 43 & 52 \\ (\text { Doha } \rightarrow \text { Dubail }) & 42 & 37 & 37 & 44 & 42 & 40 & 41 & 44 & 41 & 42 & 48 & 48 \\ \hline \end{array}$$

Explain why these are paired data.

Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The difference (After - Before) in the reasoning scores for each student has mean 3.618 and standard deviation 3.055. Construct and interpret a 90% confidence interval for the true mean difference.

A random sample of 30 words from Jane Austen's Pride and Prejudice had a mean length of 4.08 letters with a standard deviation of 2.40 letters. A random sample of 30 words from Henry James's What Maisie Knew had a mean length of 3.85 letters with a standard deviation of 2.26 letters. We wish to test the null hypothesis that the mean word length is the same in the two books. Our samples produced a 95% confidence interval for the true difference in mean word length of (-0.97, 1.43). Which of the following gives a correct conclusion for the test?

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight loss by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table provides the two estimates (in thousands of miles) for each tire.

$$\begin{array}{cccc|cccc} \hline \text { Tire } & \text { Weight } & \text { Groove } & \text { Diff. } & \text { Tire } & \text { Weight } & \text { Groove } & \text { Diff. } \\ \hline 1 & 45.9 & 35.7 & 10.2 & 9 & 30.4 & 23.1 & 7.3 \\ 2 & 41.9 & 39.2 & 2.7 & 10 & 27.3 & 23.7 & 3.6 \\ 3 & 37.5 & 31.1 & 6.4 & 11 & 20.4 & 20.9 & -0.5 \\ 4 & 33.4 & 28.1 & 5.3 & 12 & 24.5 & 16.1 & 8.4 \\ 5 & 31.0 & 24.0 & 7.0 & 13 & 20.9 & 19.9 & 1.0 \\ 6 & 30.5 & 28.7 & 1.8 & 14 & 18.9 & 15.2 & 3.7 \\ 7 & 30.9 & 25.9 & 5.0 & 15 & 13.7 & 11.5 & 2.2 \\ 8 & 31.9 & 23.3 & 8.6 & 16 & 11.4 & 11.2 & 0.2 \\ \hline \end{array}$$

Calculate the mean difference and the standard deviation of the differences. Interpret the mean difference.

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table provides the two estimates (in thousands of miles) for each tire.

$$\begin{array}{|c|c|c|c|c|c|} \hline \text { Tire } & \text { Weight } & \text { Groove } & \text { Tire } & \text { Weight } & \text { Groove } \\ \hline 1 & 45.9 & 35.7 & 9 & 30.4 & 23.1 \\ \hline 2 & 41.9 & 39.2 & 10 & 27.3 & 23.7 \\ \hline 3 & 37.5 & 31.1 & 11 & 20.4 & 20.9 \\ \hline 4 & 33.4 & 28.1 & 12 & 24.5 & 16.1 \\ \hline 5 & 31.0 & 24.0 & 13 & 20.9 & 19.9 \\ \hline 6 & 30.5 & 28.7 & 14 & 18.9 & 15.2 \\ \hline 7 & 30.9 & 25.9 & 15 & 13.7 & 11.5 \\ \hline 8 & 31.9 & 23.3 & 16 & 11.4 & 11.2 \\ \hline \end{array}$$

Construct and interpret a 95% confidence interval for the true mean difference in the estimates from these two methods (Weight - Groove) in the population of tires.

A cylindrical tank with diameter d=18 in. is subjected to internal gas pressure p=450 psi. The tank is constructed of steel sections that are welded circumferentially. The heads of the tank are hemispherical. The allowable tensile and shear stresses are 8200 psi and 3000 psi, respectively. Also, the allowable tensile stress perpendicular to a weld is 6250 psi. Determine the minimum required thickness $t_{\mathrm{min}}$ of (a) the cylindrical part of the tank and (b) the hemispherical heads.

Why did violence erupt in Kansas?

Solve the counting problem.

How many different arrangements are there for the letters in the word $KANSAS$? In $TEXAS$?

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight loss by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table provides the two estimates (in thousands of miles) for each tire.

$$\begin{array}{cccc|cccc} \hline \text { Tire } & \text { Weight } & \text { Groove } & \text { Diff. } & \text { Tire } & \text { Weight } & \text { Groove } & \text { Diff. } \\ \hline 1 & 45.9 & 35.7 & 10.2 & 9 & 30.4 & 23.1 & 7.3 \\ 2 & 41.9 & 39.2 & 2.7 & 10 & 27.3 & 23.7 & 3.6 \\ 3 & 37.5 & 31.1 & 6.4 & 11 & 20.4 & 20.9 & -0.5 \\ 4 & 33.4 & 28.1 & 5.3 & 12 & 24.5 & 16.1 & 8.4 \\ 5 & 31.0 & 24.0 & 7.0 & 13 & 20.9 & 19.9 & 1.0 \\ 6 & 30.5 & 28.7 & 1.8 & 14 & 18.9 & 15.2 & 3.7 \\ 7 & 30.9 & 25.9 & 5.0 & 15 & 13.7 & 11.5 & 2.2 \\ 8 & 31.9 & 23.3 & 8.6 & 16 & 11.4 & 11.2 & 0.2 \\ \hline \end{array}$$

Describe what the graph reveals about whether the two methods give similar estimates of tire wear, on average.

When a campfire begins to die down and smolder, you can rekindle the flame by fanning the fire. Explain, in terms of stoichiometry, why the fire again begins to flare up when fanned.