A statistics instructor wanted to see if student participation in review preparation methods led to higher examination scores. Five students were randomly selected and placed in each test group for a three-week unit on statistical inference. Everyone took the same examination at the end of the unit, and the resulting scores are shown. Is there sufficient evidence at $\alpha=0.05$ to conclude an interaction between the two factors? Is there sufficient evidence to conclude a difference in mean scores based on formula delivery system? Is there sufficient evidence to conclude a difference in mean scores based on the review organization technique?

	Formulas provided	Student-made formula cards
Student-led review	89,76,80,90,75	94,86,80,79,82
Instructor-led review	75,80,68,65,79	88,78,85,65,72

If the null hypothesis is rejected, use Scheffe's test when the sample sizes are unequal to test the differences between the means and use the Tukey test when the sample sizes are equal. For these exercises, perform these steps. Assume the assumptions have been met.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

Think of a behavior that you have that you would like to change. How could you use behavior modification, specifically positive reinforcement, to change your behavior? What is your positive reinforcer?

Considering the following data on violent crime rate (measured in violent crimes reported per $100,000$ people in the population) and state expenditure per pupil in the public schools in ten different states.

$$\begin{aligned} &\begin{array}{l|c|c} \text { State } & \begin{array}{c} \text { Violent } \\ \text { crime rate } \end{array} & \begin{array}{c} \text { Per-pupil } \\ \text { expenditure (dollars) } \end{array} \\ \hline \text { California } & 396 & 11,145 \\ \text { Connecticut } & 237 & 17,759 \\ \text { Florida } & 540 & 9223 \\ \text { Maine } & 128 & 8957 \\ \text { Mississippi } & 279 & 8779 \\ \text { New Jersey } & 261 & 20,925 \\ \text { Ohio } & 285 & 11,530 \\ \text { Tennessee } & 608 & 8809 \\ \text { Utah } & 216 & 7711 \\ \text { Wisconsin } & 290 & 11,424 \end{array}\\ &\text { Soures: National Center for Education Statistics, 2015; FBI, } 2014 . \end{aligned}$$

a. Make a scatterplot of the data. b. Do the variables in the data set appear to be correlated? Express the correlation in words. c. If you are using Excel, add a best-fit line (also called a trend line) to the scatterplot.

For some years, the City of Armstrong Power Authority has used 4-20 mA technology to measure parameters such as pressure, temperature, flow rates, and speed of various machinery and systems installed in its generation facilities. It now plans to use the same technology to measure vibration on all of its rotating machinery with the goal of evaluating continuously the health of the equipment, to include friction buildup, breakdown prediction, and preventive maintenance needs. Depending upon the vendors chosen, the useful lives and anticipated annual net savings will vary, as reflected in the estimates shown.

$$\begin{array}{lcccc} \text { Vendor } & 1 & 2 & 3 & 4 \\ \hline \text { Investment, } \$ 1000 & -500 & -700 & -900 & -1000 \\ \text { Life, years } & 5 & 5 & 3 & 4 \\ \hline \end{array}$$

$$\begin{matrix} \text{ } & \text{ } & \text{ } & \text{Vendor} & \text{ }\\ \hline \text{ } & \text{1} & \text{2} & \text{3} & \text{4}\\ \hline \text{Year} & \text{ } & \text{Savings Estimates,} & \text{\$1000 per Year} & \text{ }\\ \hline \text{1} & \text{100} & \text{50} & \text{500} & \text{0}\\ \text{2} & \text{170} & \text{50} & \text{500} & \text{0}\\ \text{3} & \text{240} & \text{50} & \text{200} & \text{0}\\ \text{4} & \text{300} & \text{50} & \text{ } & \text{1800}\\ \text{5} & \text{380} & \text{1000} & \text{ } & \text{ }\\ \hline \end{matrix}$$

Develop the linear programming model and use a spreadsheet to select the vendor(s) that offer the best opportunity economically. The city’s MARR is 5% per year and the investment limit is $1,600,000.

The United States imposes an excise tax on the sale of domestic airline tickets. Let's assume that in 2015 the total excise tax was $\$ 6.10$ per airline ticket (consisting of the $3.60 flight segment tax plus the $2.50 September$11 $\mathrm{fee} ). According to data from the Bureau of Transportation Statistics, in 2015, 643 million passengers traveled on domestic airline trips at an average price of$$380$ per trip. The accompanying table shows the supply and demand schedules for airline trips. The quantity demanded at the average price of $\$ 380$ is actual data; the rest is hypothetical.

a. What is the government tax revenue in 2015 from the excise tax?

b. On January 1,2016 , the total excise tax increased to $\$ 6.20$ per ticket. What is the quantity of tickets transacted now? What is the average ticket price now? What is the 2016 government tax revenue?

c. Does this increase in the excise tax increase or decrease government tax revenue?

Weakening a behavior through the withdrawal of reinforcement for that behavior is called as ________. In general, this is a (slower/faster) procedure than punishment.

Exam scores of 40 students in a statistics class are shown.

(a) Estimate the mean and standard deviation from the sample.

(b) Assuming that the data are from a normal distribution, define bins by using method 3 (equal expected frequencies). Use 8 bins.

(c) Set up an Excel worksheet for your chi-square calculations, with a column showing the expected frequency for each bin (they must add to 40).

(d) Tabulate the observed frequency for each bin and record it in the next column.

(e) Carry out the chi-square test, using $\alpha=.05$. Can you reject the hypothesis that the exam scores came from a normal population?

$$\begin{array}{llllllll}79 & 75 & 77 & 57 & 81 & 70 & 83 & 66 \\ 81 & 89 & 59 & 83 & 75 & 60 & 96 & 86 \\ 78 & 76 & 71 & 78 & 78 & 70 & 54 & 60 \\ 71 & 81 & 79 & 88 & 77 & 82 & 75 & 68 \\ 77 & 69 & 83 & 79 & 79 & 76 & 78 & 71\end{array}$$

Compare Romeo's behavior before he meets Juliet with his behavior after they declare their love for each other. What do you learn about Romeo from the change in his behavior?

Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits Lower limit: $Q_{1}-1.5 \times(I Q R)$ Upper limit: $Q_{3}+1.5 \times(I Q R)$ where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were

$$\begin{array}{cccccccccccc} 65 & 72 & 68 & 64 & 60 & 55 & 73 & 71 & 52 & 63 & 61 & 74 \\ 69 & 67 & 74 & 50 & 4 & 75 & 67 & 62 & 66 & 80 & 64 & 65 \end{array}$$

(b) Find the value of the interquartile range (IQR).

Sonic, Inc., sells business software. Currently, all of its programs come on disks. Due to their complexity, some of these applications occupy as many as seven disks. Not only are the disks cumbersome for customers to load, they are relatively expensive for Sonic to purchase. The company does not intend to discontinue using disks altogether. However, it does want to reduce its reliance on the disk medium.

Two proposals are being considered. The first is to provide software on computer chips. Doing so requires a $\$ 300,000$ investment in equipment. The second is to make software available through a computerized "software bank." In essence, programs would be downloaded directly from Sonic using telecommunications technology. Customers would gain access to Sonic's mainframe, specify the program they wish to order, and provide their name, address, and credit card information. The software would then be transferred directly to the customer's hard drive, and copies of the user's manual and registration material would be mailed the same day. This proposal requires an initial investment of $\$ 240,000$.

The following information pertains to the two proposals. Due to rapidly changing technology, neither proposal is expected to have any salvage value or an estimated life exceeding six years.

$$\begin{array}{lrr} & \text{Computer Chip Equipment} & \text{Software Bank Installation}\\ \hline \text{\text { Estimated incremental annual revenue of investment }}\ldots &\$ 300,000 &\$ 160,000\\ \text{Estimated incremental annual expense of investment} \ldots & & \\ \text{ (including taxes and depreciation)} & 250,000& 130,000\\ \end{array}$$

The only difference between Sonic's incremental cash flows and its incremental income is attributable to depreciation. A minimum return on investment of 15 percent is required.

What nonfinancial factors should be considered?

In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.

$$\begin{array}{llll} \text { Highest education } & \text {Total population } & \text { In labor force} & \text { Employed } \\ \hline \begin{array}{l} \text { Didn't finish high } \\ \text { school } \end{array} & 27,669 & 12,470 & 11,408 \\ \begin{array}{l} \text { High school but no } \\ \text { college } \end{array} & 59,860 & 37,834 & 35,857 \\ \begin{array}{l} \text { Less than } \\ \text { bachelor's degree } \end{array} & 47,556 & 34,439 & 32,977 \\ \text { College graduate } & 51,582 & 40,390 & 39,293 \\ \hline \end{array}$$

Suppose that you randomly select one person 25 years of age or older. If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he or she is in the labor force?

Discuss the differences between a system that exhibits chaotic behavior and one whose behavior is purely random. Is there a difference?

The following table is based on a summary of a survey conducted by the Bureau of Labor Statistics. There are wide differences in the median wages of the occupations listed—for example, between air traffic controllers and actors. (Half the workers in an occupation earn more than the median wage and half earn less.) But there are also significant variations in wages within occupations. The highest-paid workers in any of the occupations earned more than the lowest-paid workers in any of the other occupations. For each of the following occupations, provide one reason large variations exist between the tenth and ninetieth percentile wages:

Athletes

The data in the given table were collected from one of the statistics classes. The first row gives the variable, and each of the other rows represents a student in the class.

Find the frequency, proportion, and percentage of brown-haired people in the Table?