A track coach wants to compare the 200m time of his high school track team.
boy: 23, 22, 21, 24, 23, 25, 22, 23
girl: 25, 28, 22, 26, 29, 26, 27, 24

a. What test should he use to compare the means?
b. Is it significant at 0.5 level?
c. What conclusion can be made?
d. Calculate omega squared and interpret its meaning in this study.

t = (M₁-M₂)/sqr rt [{(N₁-1)S_{1² +} (N₂-1)S2²/(N₁+N₂-2)] _* [(N_{1 +} N₂)/N1*N2]}

Ω² = {(t² - 1)/ (t² + N₁ + N₂ -1)} X 100

Develop a snack bar for a local high school football stadium. You have an empty shell of a small room (measuring ten feet by 15 feet). You currently have no cooking instruments, but you have an ice maker and cash register that you do not need to pay for. Your task is to buy equipment, based on what you want to sell, and then you have to buy products to sell. You need to look at actual prices (you can buy some food at Costco as an example). You have to develop a budget that takes into consideration fixed costs and variable costs and then the revenue you anticipate making. I want this to be as real world as possible so you have to think about whether your budget is realistic and if you have covered everything. Imagine if you work at the high school and if screw-up you can be fired. You want to maximize revenue, but minimize costs. The key is to think about what you will offer, how you will offer it, how will you deliver, produce, etc… everything before you start buying. As an example, you need to clean the snack bar after every game which requires you buy cleaning supplies. Another component is identifying what are fixed costs and what are variable costs.

The following table gives data from a local school district on children's ages (x) in years and reading levels(y). Age in years X: 6, 7, 8, 9, 10, 11, 12, 14, 14, 15. Reading level Y: 1.3, 2.2, 3.7, 4.1, 4.9, 5.2, 6.0, 7.1, 8.5, 9.7.
Calculate the correlation coefficient r.
Calculate the coefficient of determination r2. Find the regression coefficients and estimate the regression equation.   
Based on the estimated regression equation in (b), find the reading level of a child who is 9.5 years.

Isabelle Abiassi operates a popular summer camp for elementary school children. Projections for the current year are as follows:

The camp’s weighted-average cost of capital is 11%, and Isabelle requires that all new investments generate a return on investment of at least 15%. The camp’s current tax rate is 25%.

At last week’s advisory board meeting, Isabelle told the board that she had up to $50,000 to invest in new facilities at the camp and asked them to recommend some projects. Today the board’s president presented Isabelle with the following list of three potential investments to improve the camp facilities.

Calculate the return on investment, residual income, and economic value added for each of the three projects.

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 82 students shows that 36 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

What are we testing in this problem?

single proportionsingle mean    

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.35; H₁: p > 0.35H₀: μ = 0.35; H₁: μ < 0.35    H₀: p = 0.35; H₁: p < 0.35H₀: p = 0.35; H₁: p ≠ 0.35H₀: μ = 0.35; H₁: μ > 0.35H₀: μ = 0.35; H₁: μ ≠ 0.35

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since np > 5 and nq > 5.The standard normal, since np > 5 and nq > 5.    The Student's t, since np < 5 and nq < 5.The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250    0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.There is insufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.    

A survey conducted at Chicago Public Schools (CPS) involving high school students on whether they had participated in binged drinking during the past month. Binge drinking was defined as 5 or more drinks in a row on one or more of the past 30 days.

a. From the sample data is there evidence that the proportion of students who participate in binge drinking is greater than 10%? Write a null and alternative hypothesis and perform an appropriate significance test using

b. Construct a 90% Confidence Interval for the population proportion. Does it support the same conclusion as in part a? Explain.

John was a high school teacher earning $ 80,000 per year. He quit his job to start his own business in pizza catering.In order to learn how to run the pizza catering business, John enrolled in a TAFE to acquire catering skills.John’s course was for 3 months. John had to pay $2,000 as tuition for the 3 months.

After the training, John withdrew $110,000 from his savings account. He had been earning 5 percent interest per year for this account. He also borrowed $50,000.00 from his friend whom he pays 6 percent interest per year. Further, to start the business John used his own premises. He was receiving $12,000from rent per year. Finally, to start the business John uses $50,000 he had been given by his father to go on holiday to USA.

John’s first year of business can be summarised as follows:

Based on your calculated accounting profit and economic profit, would you advise John to return to his teaching job? Show your work    

Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 83students shows that 38 have jobs. Do the data indicate that more than 35% of the students have jobs? Use a 5% level of significance.

What are we testing in this problem?

single mean

single proportion     

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.35; H₁: p > 0.35

H₀: μ = 0.35; H₁:  μ < 0.35     

H₀: p = 0.35; H₁:  p < 0.35

H₀: μ = 0.35; H₁: μ > 0.35

H₀: p = 0.35; H₁:  p ≠ 0.35

H₀: μ = 0.35; H₁:  μ ≠ 0.35

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal, since np > 5 and nq > 5.

The Student's t, since np < 5 and nq < 5.     

The Student's t, since np > 5 and nq > 5.

The standard normal, since np < 5 and nq < 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.250

0.125 < P-value < 0.250     

0.050 < P-value < 0.125

0.025 < P-value < 0.050

0.005 < P-value < 0.025

P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.     

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.

There is insufficient evidence at the 0.05 level to conclude that more than 35% of the students have jobs.

Physical activity generally declines when students leave high school and enroll in college. This suggests that college is an ideal setting to promote physical activity. One study examined the level of physical activity and other health-related behaviors in a sample of 1183 college students. Let's look at the data for physical activity and consumption of fruits. We categorize physical activity as low, moderate, or vigorous and fruit consumption as low, medium, or high. Here is the two-way table that summarizes the data.

The first step in performing the significance test is to calculate the expected cell counts. Let's start with the cell for students with low fruit consumption and low physical activity. Use the following formula for expected cell counts.expected count =

Using the formula, we need three quantities:

(1) the corresponding row total, 568, the number of students who have low fruit consumption,
(2) the column total,  , the number of students who have low physical activity, and
(3) the total number of students, 1183.

The expected cell count is therefore the following.

= 51.37Note that although any observed count of the number of students must be a whole number, an expected count need not be.

Calculations for the other eight cells in the 3 ✕ 3 table are performed in the same way. With these nine expected counts we are now ready to use the following formula for the  χ² statistic.χ² =

The first term in the sum comes from the cell for students with low fruit consumption and low physical activity. The observed count is  and the expected count is 51.37. Therefore, the contribution to the χ ² statistic for this cell is the following.

= 5.38When we add the terms for each of the nine cells, the result is the following. (Round your answer to two decimal places.)

χ ² =

Because there are

r = 3

levels of fruit consumption and

c =

levels of physical activity, the degrees of freedom for this statistic are the following.df = (r − 1)(c − 1) = (3 − 1)

  − 1

= Under the null hypothesis that fruit consumption and physical activity are independent, the test statistic χ ² has a χ ²

distribution. To obtain the P-value, look at the

df =

row in Table F. The calculated value

χ ² =

lies between the critical points for probabilities 0.005 and 0.01. The P-value is therefore between 0.005 and 0.01. (Software gives the value, rounded to four decimal places, as 0.0081.) There  ---Select--- is is not strong evidence at α = 0.01 that there is a relationship between fruit consumption and physical activity.

The data below provides College GPA, High School GPA, SAT total score, and a number of letters of reference. a.Generate a model for college GPA as a function of the other three variables? b.Is this model useful? Justify your conclusion. c.Are any of the variables not useful predictors? Why? CGPA HSGPA SAT REF 2.04 2.01 1070 5 2.56 3.4 1254 6 3.75 3.68 1466 6 1.1 1.54 706 4 3 3.32 1160 5 0.05 0.33 756 3 1.38 0.36 1058 2 1.5 1.97 1008 7 1.38 2.03 1104 4 4.01 2.05 1200 7 1.5 2.13 896 7 1.29 1.34 848 3 1.9 1.51 958 5 3.11 3.12 1246 6 1.92 2.14 1106 4 0.81 2.6 790 5 1.01 1.9 954 4 3.66 3.06 1500 6 2 1.6 1046 5 2.05 1.96 1054 4 2.6 1.96 1198 6 2.55 1.56 940 3 0.38 1.6 456 6 2.48 1.92 1150 7 2.74 3.09 636 6 1.77 0.78 744 5 1.61 2.12 644 5 0.99 1.85 842 3 1.62 1.78 852 5 2.03 1.03 1170 3 3.5 3.44 1034 10 3.18 2.42 1202 5 2.39 1.74 1018 5 1.48 1.89 1180 5 1.54 1.43 952 3 1.57 1.64 1038 4 2.46 2.69 1090 6 2.42 1.79 694 5 2.11 2.72 1096 6 2.04 2.15 1114 5 1.68 2.22 1256 6 1.64 1.55 1208 5 2.41 2.34 820 6 2.1 2.92 1222 4 1.4 2.1 1120 5 2.03 1.64 886 4 1.99 2.83 1126 7 2.24 1.76 1158 4 0.45 1.81 676 6 2.31 2.68 1214 7 2.41 2.55 1136 6 2.56 2.7 1264 6 2.5 1.66 1116 3 2.92 2.23 1292 4 2.35 2.01 604 5 2.82 1.24 854 6 1.8 1.95 814 6 1.29 1.73 778 3 1.68 1.08 800 2 3.44 3.46 1424 7 1.9 3.01 950 6 2.06 0.54 1056 3 3.3 3.2 956 8 1.8 1.5 1352 5 2 1.71 852 5 1.68 1.99 1168 5 1.94 2.76 970 6 0.97 1.56 776 4 1.12 1.78 854 6 1.31 1.32 1232 5 1.68 0.87 1140 6 3.09 1.75 1084 4 1.87 1.41 954 2 2 2.77 1000 4 2.39 1.78 1084 4 1.5 1.34 1058 4 1.82 1.52 816 5 1.8 2.97 1146 7 2.01 1.75 1000 6 1.88 1.64 856 4 1.64 1.8 798 4 2.42 3.37 1324 6 0.22 1.15 704 6 2.31 1.72 1222 5 0.95 2.27 948 6 1.99 2.85 1182 8 1.86 2.21 1000 6 1.79 1.94 910 6 3.02 4.25 1374 9 1.85 1.83 1014 6 1.98 2.75 1420 7 2.15 1.71 400 6 1.46 2.2 998 7 2.29 2.13 776 6 2.39 2.38 1134 7 1.8 1.64 772 4 2.64 1.87 1304 6 2.08 2.53 1212 4 0.7 1.78 818 6 0.89 1.2 864 2