What conditions are required for valid large-sample inferences about

$$\mu _ { d } ?$$

small-sample inferences?

What conditions are required for a valid large-sample test for

$$\mu ?$$

To use the t -statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?

What conditions are required for valid inferences from a factorial ANOVA?

In a paired difference experiment, when should the observations be paired, before or after the data are collected?

From the list below, supply the words needed to complete the paragraph. Some words will not be used.

$$\begin{array}{llll}\text { sapient } & \text { idiosyncrasy } & \text { blanch } & \text { machination } \\ \text { pejorative } & \text { masochist } & \text { nubile } & \text { deride } \\ \text { heterogeneous } & \text { grandiose } & \text { raiment } & \text { finesse }\end{array}$$

Dr. Quade still wore the ______ of a maximum-security prison inmate when he entered an abandoned warehouse to evade the searchlights of police helicopters. Six years of living without sunlight in an underground cell had ______ the color of his face, and the beatings and ______ treatment that he received from guards had left him with a perpetual scowl. Now, he mused, he would be free to carry out the ______ that he had planned during his confinement, but not before using his criminal ______ to steal an automobile from the nearby parking garage. The garage contained a[n] ______ collection of automobiles, but the ______ Dr. Quade chose a very dull, plain car to hotwire; a[n] ______ car could draw unwanted attention that jeopardized the escape.

Even without keys, the mad genius was able to start the car in two minutes; however, he revealed a violent ______ by punching the dashboard when a light indicated that the car was low in fuel. The resulting cuts on his hands would have irritated a normal person, but not a[n] ______ like Dr. Quade. As he drove out of the garage, Dr. Quade allowed himself a chuckle as he ______ the system that had mistakenly thought it could keep him imprisoned.

Solve the equation.

$$\sqrt [ 3 ] { x - 2 } = 2$$

A pot of boiling water is allowed to cool for 50 minutes. The table below shows the temperature of the water as it cools. Use the table for the problem below.

$$\begin{matrix} \text{Temperature of Water} (y_d), \text{in degrees Celsius, after cooling for x minutes} & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & \text{ }\\ \text{x} & \text{0} & \text{5} & \text{10} & \text{15} & \text{20} & \text{25} & \text{30} & \text{35} & \text{40} & \text{45} & \text{50}\\ y_d & \text{100} & \text{75} & \text{57} & \text{44} & \text{34} & \text{26} & \text{21} & \text{17} & \text{14} & \text{11} & \text{10}\\ y_m\\ \text{residual}\\ \end{matrix}$$

Examine the residuals in each table. Which appears to be the better model—the linear or exponential equation? Explain.

Two populations are described in each of the cases that follow. In which cases would it be appropriate to apply the small-sample t -test to investigate the difference between the population means? Population 1: Normal distribution with variance

$$\sigma _ { 1 } ^ { 2 }$$

2 Population 2: Skewed to the right with variance

$$\sigma _ { 2 } ^ { 2 } = \sigma _ { 1 } ^ { 2 }$$

Impact of red light cameras on car crashes. To combat red-light-running crashes many states have installed red light cameras at dangerous intersections to photograph the license plates of vehicles that run the red light. How effective are photo-red enforcement programs in reducing red-light-running crash incidents at intersections? The Virginia Department of Transportation (VDOT) conducted a comprehensive study of its photo-red enforcement program. In one portion of the study, the VDOT provided crash data both before and after installation of red light cameras at several intersections. The data (measured as the number of crashes caused by red light running per intersection per year) for 13 intersections in Fairfax County, Virginia, are given in the table. Analyze the data for the VDOT. What do you conclude?

In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06. a. Assume that p is near .3. b. Assume that you have no prior knowledge about p , but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

Compute the Taylor series of the function around x = 1. $f(x)=\frac{1}{x}$

According to a University of Florida wildlife ecology and conservation researcher, the average level of mercury uptake in wading birds in the Everglades has declined over the past several years. ( UF News , December 15, 2000). Ten years ago, the average level was 15 parts per million. a. Give the null and alternative hypotheses for testing whether the average level today is less than 15 ppm. b. Describe a Type I error for this test. c. Describe a Type II error for this test.

Triangle ABC has vertices A(2,1), B(-6, 5), and C(-2, -3). Describe any relationship between the lengths of the sides of the two triangles.