COURSE TITLE: STATISTICS

CHAPTER 1: WHAT IS STATISTICS?

Exercise 1: The age of each person in a sample of 50 adults who listen to one of the 1,230 talk radio stations in the United States is:

35 29 41 34 44 46 42 42 37 47

30 36 41 39 44 39 43 43 44 40

47 37 41 27 33 33 39 38 43 22

44 39 35 35 41 42 37 42 38 43

35 37 38 43 40 48 42 31 51 34

What is the level of measurement reflected by the above data?

Exercise 2: In a survey of 200 luxury-car owners, 100 were from California, 50 from New York, 30 from Illinois, and 20 from Ohio.

What is the level of measurement reflected by the above data?

CHAPTER 2: DESCRIBING DATA - Frequency Distributions and Graphic Presentation

Exercise 1: The prices of Hyundai Santa Fe sold last month at Whitner Autoplex are:

23,197 USD 24,220 USD 22,845 USD

18,021 USD 21,556 USD 22,374 USD

20,047 USD 23,372 USD 30,655 USD

19,873 USD 28,683 USD 21,639 USD

20,004 USD 24,285 USD 20,454 USD

20,203 USD 25,251 USD 30,872 USD

24,052 USD 17,357 USD 24,324 USD

20,356 USD 23,765 USD 25,277 USD

20,962 USD 25,799 USD 20,155 USD

21,740 USD 21,442 USD 25,783 USD

1. How many classes would you use?

2. What class interval would you suggest?

Exercise 2: Relative frequency distribution of the prices of Hyundai Santa Fe sold last month at Whitner Autoplex is:

Selling price (unit: thousand USD) Frequency

15 up to 18 8

18 up to 21 23

21 up to 24 17

24 up to 27 18

27 up to 30 8

30 up to 33 4

33 up to 36 2

1. How many vehicles were sold for 18,000 USD up to 21,000 USD?

2. What percent of the vehicles sold for a price between 18,000 USD and 21,000 USD?

3. What percent of the vehicles sold for 30,000 USD or more?

CHAPTER 3: DESCRIBING DATA - Numerical Measures

Exercise 1: Last month the High-Tech Supermarket sold 95 computers for the price of 400USD (400 USD/computer), 126 computers for the price of 200 USD, and 79 computers for the price of 100 USD. What was the weighted mean price of a computer?

Exercise 2: The sales at Cosmetics Store increased 4.91% in 2005, 5.75% in 2006, 8.12% in 2007 and 21.60% in 2008. What is the geometric mean percent increase?

Exercise 3: The production of Isuzu trucks increased from 23,000 units in 1984 to 120,520 units in 2004. What is the geometric mean annual percent increase?

Exercise 4: The weights of 8 containers to be shipped to Ireland are

95 tons 110 tons 112 tons

103 tons 104 tons 90 tons

105 tons 105 tons

1. What is the range of the weights?

2. Compute the arithmetic mean weight.

3. Compute the mean deviation of the weight.

Exercise 5: The monthly salaries of 5 employees at Lotus Department Store are as follows:

3,536 USD 3,173 USD 3,448 USD 3,121 USD 3,622 USD

1. Compute the population variance.

2. Compute the population standard deviation.

Exercise 6: The weight of the contents of several small aspirin bottles are as follows:

4 grams 5 grams 5 grams 6 grams

2 grams 4 grams 2 grams

1. Compute the sample variance.

2. Determine the sample standard deviation.

CHAPTER 5: A SURVEY OF PROBABILITY CONCEPTS

Exercise 1: Suppose you are going to survey about a new pension plan. You are going to take a sample of 2,000 employees. The employees are classified as follows:

Classification Event Number of Employees

Supervisors A 120

Maintenance B 50

Production C 1,460

Management D 302

Secretarial E 68

1. What is the probability that the first person selected is: either in maintenance or a secretary?

2. What is the probability that the first person selected is not in management?

Exercise 2: There are 12 rolls of film in a box, 8 of which are defective. 4 rolls are to be selected, one after the other, without being returned to the box. What is the probability all 4 rolls of film are defective?

CHAPTER 8: SAMPLING METHODS AND THE CENTRAL LIMIT THEOREM

Exercise 1: The Quality Assurance Department for Cola, Inc. maintains the records regarding the amount of cola in the bottle. Their records indicate that the amount of cola follows the normal probability distribution. The mean amount per bottle is 31.2 ounces and the population standard deviation is 0.4 ounces. At 8:00 AM today the quality technician randomly selected 16 bottles from the filling line. The mean amount of cola contained in the bottles is 31.08 ounces. What can you conclude about the filling process?

Exercise 2: The mean hourly wage for plumbers in the Atlanta region is 28 USD. What is the likelihood that we could select a sample of 50 plumbers with a mean wage of 28.5 USD or more? The standard deviation of the sample is 2 USD per hour.

CHAPTER 9: ESTIMATION AND CONFIDENCE INTERVAL

Exercise 1: The mean daily sales at the Bun-and-Run (a fast food restaurant) is 20,000 USD for a sample of 40 days. The standard deviation of the sample is 3,000 USD.

1. What is the estimated mean daily sale of the population (the mean daily sales for all days)? What is this estimate called?

2. What is the 99 percent confidence interval?

3. Interpret your findings.

Exercise 2: The Dottie Restaurant bakes and sells cookies at 50 different locations in the Philadelphia area. The manager of this restaurant is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week day period.

4 1 2 2 1 2 2 1 0 3

1. What is the population mean? What is the best estimate of that value?

2. Develop a 95 percent confidence interval for the population mean.

Exercise 3: The owner of the West Gas Station wished to determine the proportion of customers who use a credit card to pay at the pump. He surveys 1,400 customers and finds that 420 used credit cards to pay at the pump.

1. Estimate the value of the population proportion.

2. Compute the standard error of the proportion.

3. Develop a 99 percent confidence interval for the population proportion.

4. Interpret your findings.

CHAPTER 10: ONE-SAMPLE TESTS OF HYPOTHESIS

Exercise 1: The following information is available

H0:

H1:

The sample mean is 49, and the sample size is 36. The population standard deviation is 5. Use the 0.05 significance level.

1. Is this a one-tailed or two-tailed test?

2. What is the decision rule?

3. What is the value of the test statistic?

4. What is your decision regarding H0?

Exercise 2: The following information is available

H0:

H1:

A sample of 36 observations is selected from a normal population. The sample mean is 21, and the standard deviation is 5. Use the 0.05 significance level.

1. Is this a one-tailed or two-tailed test?

2. What is the decision rule?

3. What is the value of the test statistic?

4. What is your decision regarding H0?

Exercise 3: The following hypotheses are given

H0:

H1:

A sample of 100 observations revealed that p = 0.75. At the 0.05 significance level, can the null hypothesis (H0) be rejected?

1. State the decision rule.

2. Compute the value of the test statistic

3. What is your decision regarding the null hypothesis (H0)?

Exercise 4: Given the following hypothesis:

H0:

H1:

For a random sample of 10 observations, the sample mean was 12 and the sample standard deviation is 3. Using the 0.05 significance level.

1. State the decision rule.

2. Compute the value of the test statistic

3. What is your decision regarding the null hypothesis (H0)?

CHAPTER 11: TWO-SAMPLE TESTS OF HYPOTHESIS

Exercise 1: A sample of 40 observations is selected from one population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second population. The sample mean is 99 and the sample standard deviation is 6. Conduct the following test of hypothesis using the 0.04 significance level.

H0:

H1:

1. Is this a one-tailed or a two-tailed test?

2. State the decision rule.

3. Compute the value of the test statistic

4. What is your decision regarding the null hypothesis (H0)?

Exercise 2: The null and alternate hypotheses are:

H0:

H1:

A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed X2 to be 90. Use the 0.05 significance level to test the hypothesis.

1. State the decision rule.

2. Compute the pooled proportion.

3. Compute the value of the test statistic.

4. What is your decision regarding the null hypothesis (H0)?

Exercise 3: A sample of scores on an examination of the course "Advanced English" are:

Men 72 69 98 66 85 76 79 80 77

Women 81 67 90 78 81 80 76

At the 0.01 significance level, is the mean grade of the women higher than the mean grade of the men?

Exercise 4: The null and alternate hypotheses are:

H0:

H1:

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of 4 days last month.

Day 1 Day 2 Day 3 Day 4

Day shift 10 12 15 19

Afternoon shift 8 9 12 15

At the 0.05 significance level, can we conclude there are more defects produced on the afternoon shift?

CHAPTER 12: ANALYSIS OF VARIANCE

Exercise 1: The following hypotheses are given

H0:

H1:

A random sample of 8 observations from the first population resulted in a standard deviation of 10. A random sample of 6 observations from the second population resulted in a standard deviation of 7. At the 0.02 significance level, is there a difference in the variation of the two population?

Exercise 2: The following is sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 significance level.

Treatment 1 Treatment 2 Treatment 3

8 3 3

6 2 4

10 4 5

9 3 4

1. State the null hypothesis and the alternate hypothesis.

2. What is the decision rule?

3. Complete the following ANOVA table.

Source of Variation Sum of Squares

(SS) Degrees of Freedom

(df) Mean Square

(MS) F

Treatment 62.17

Error

Total 74.92

4. State your decision regarding the null hypothesis.

Exercise 2: The following data are given for a two-factor ANOVA

Block Treatment

1 2 3

A 31 25 35

B 33 26 33

C 28 24 30

D 30 29 28

E 28 26 27

Using 0.05 significance level, conduct a test of hypothesis to determine whether the block or the treatment means differ.

1. State null hypothesis and alternate hypothesis for treatments.

2. State the decision rule for treatments

3. State null hypothesis and alternate hypothesis for blocks.

4. State the decision rule for blocks.

5. Complete the following ANOVA table.

Source of Variation Sum of Squares

(SS) Degrees of Freedom

(df) Mean Square

(MS) F

Treatments 62.53

Blocks

Error 43.47

Total 139.73

6. Give your decision regarding the two sets of hypotheses.

CHAPTER 13: LINEAR REGRESSION AND CORRELATION

Exercise 1: The following sample observations were randomly selected.

X: 4 5 3 6 10

Y: 4 6 5 7 7

Given that the standard deviation of Y is 1.3038, the standard deviation of X is 2.7019, and coefficient of correlation is 0.7522.

1. Determine the regression equation.

2. Determine the value of Y' when X is 7.

Exercise 2: Given the following ANOVA table

SOURCE DF SS MS F

Regression 1 1000 1000 26.00

Error 13 500 38.46

Total 14 1500

1. Determine the coefficient of determination.

2. What is the coefficient of correlation?

3. Determine the standard error of estimate.

CHAPTER 14: MULTIPLE REGRESSION AND CORRELATION ANALYSIS

Exercise 1: The director of marketing at a computer company is studying monthly sales. Three variables are thought to relate to the monthly sale (Y). These three variables are: regional population (X1), per-capita income (X2), and regional unemployment rate (X3). The regression equation was computed to be (in USD): Y' = 64,100 + 0.394X1 + 9.6X2 - 11,600X3

1. What is the full name of the equation?

2. Interpret the number 64,100

3. What are the estimated monthly sales for a particular region with a population of 796,000 people, per-capita income of 6,940 USD, and an unemployment rate of 6 percent.

4. The following output was obtained

SOURCE SS DF MS F

Regression 3.8479 1 3.8479 3.91

Residual 2.9521 3 0.9840

Total 6.8000 4

Compute and interpret

Exercise 2: Refer to the following ANOVA table

SOURCE DF SS MS F

Regression 3 21 7.0 2.33

Error 15 45 3.0

Total 18 66

1. How large was the sample?

2. How many independent variables are there?

3. Compute the coefficient of multiple determination.

4. Compute the multiple standard error of estimate.

Exercise 3: The following output was obtained

SOURCE DF SS MS F

Regression 5 100 20

Error 20 40 2

Total 25 140

Predictor Coef StDev t-ratio

Constant 3.00 1.50 2.00

X1 4.00 3.00 1.33

X2 3.00 0.20 15.00

X3 0.20 0.05 4.00

X4 -2.50 1.00 -2.50

X5 3.00 4.00 0.75

1. What is the sample size?

2. Compute the value of r2?

3. Conduct a global test of hypothesis to determine whether any of the regression coefficients are significant. Use the 0.05 significance level.

4. Test the regression coefficients individually. Would you consider obmiting any variables? If so, which one? Use the 0.05 significance level.