# General Statistics

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Define the term "hypothesis"; what is a hypothesis test?

2. List and describe two types of error that can occur in hypothesis testing.

3. An independent testing laboratory has been commissioned to determine the relative fuel economy of cars, light trucks, and sport utility vehicles. A random sample of 200 within each category will be taken and their overall miles per gallon will be measured on a controlled course at different speeds. Discuss the nature of the hypothesis on the basis of the type of data (quantitative or qualitative) that is being analyzed and how the population(s) can be compared.

4. List the five steps required to test a hypothesis of the mean. Be sure that all steps are in the correct sequence.

5. The employees of Jones Construction Co. are allowed a 30-minute lunch break. The owner wants to know if the employees are actually taking 30-minute breaks. The foreman decides to record the times taken for the next 25 breaks taken at the site. The data are as follows:

25 34 28 27 33 40 23 22 26

33 38 25 22 27 30 32 31 24

22 28 32 34 26 24 35

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic.

c. At  = 0.05, should the foreman reject the null hypothesis?

d. What conclusion can the foreman present to the owner?

6. The players on last year's football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team's average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team's progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:

346 412 332 285 396 461 321 275

246 315 298 347 430 419 406 311

319 385 377 365 385 400

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic.

c. At  = 0.01, should Coach Juarez reject the null hypothesis?

d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?

7. Nielsen Media Research reported that in 1998, 70% of the households in the nation owned at least one working television set. Suppose that you conduct a survey of 150 households in your city and discover that 73% of the households owned a working television set. Does your city differ from the rest of the nation?

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic and find the p value.

c. At  = 0.05, do you reject the null hypothesis?

d. What conclusion can you draw?

8. Complete the following table to illustrate your understanding of the hypotheses tests needed to compare two population means:

Two-Sided Test

H0: 1 = 2 or H0:

HA: HA:

Lower-Tail Test

H0: or H0:

HA: 1 < 2 HA:

Upper-Tail Test

H0: or H0:

HA: HA: 1  2 > 0

9. A supermarket chain just added two new stores located on opposite sides of a city. Management is interested in determining if customers are spending an equal time shopping in the stores. The research team temporarily installed a clock punch in each store and asked 100 customers at each location to collect a time card and punch in when they arrived and punch out as they left with their sacks full of groceries. Results from the time cards are summarized in the table below:

Store 1 Store 2

Mean Shopping Time (min.)

Standard Deviation (min.) 89.3

6.6 83.5

7.1

Test the hypothesis that the two means are the same at  = 0.05 versus the alternative hypothesis that the two means are not the same.

10. George Harris is trying to decide between two on-line investment companies to handle his stock transactions. George has decided that he will open an account with the company that can process his transaction requests the fastest. Data measuring the average transaction time for the past 42 days of trading are shown below for each company:

Company 1 Company 2

Mean Transaction Time (min.)

Standard Deviation (min.) 4.35

1.6 4.85

1.1

Test the hypothesis that the two means are the same at  = 0.05 versus the alternative hypothesis that the two means are not the same.

11. A diaper company is considering 3 different filler materials for their disposable diapers. Eight diapers were tested with each of the 3 filler materials and 24 toddlers were randomly given a diaper to wear. As the child played, fluid was injected into to diaper every 10 minutes until the product failed (leaked). The amount of fluid (in grams) at the time of failure was recorded for each diaper. The data are shown below:

Material 1 Material 2 Material 3

791 809 828

789 818 814

796 803 855

802 781 844

810 813 847

790 808 848

800 805 836

790 811 873

a). What is the response variable and what is the factor?

b) How many levels of the factor are being studies?

c) Is there any difference in the amount of fluid the diaper can hold using the 3 different materials? If so, which ones are different?

d) What is your recommendation to the company?

12. Does a heavier bowler knock down more pins? Jim Samuels, manager of Maple Lanes, asked 15 men's league players to report their body weight (lbs) and their league average, rounded to the nearest pin. Results are shown below:

Weight, X Average, Y Weight, X Average, Y

154 156 215 159

159 145 226 152

165 178 237 132

172 201 245 178

178 205 262 196

192 191 280 145

205 187 289 168

211 146

a. Construct a scatter plot of the data

b. Find the equation for the least squares line of best fit

c. Draw the least squares line on the scatter plot

d. Predict the league average for an adult male bowler who weighs 190 lbs.

What can you conclude?

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##### Solution Summary

Define the term "hypothesis"; what is a hypothesis test?

2. List and describe two types of error that can occur in hypothesis testing.

3. An independent testing laboratory has been commissioned to determine the relative fuel economy of cars, light trucks, and sport utility vehicles. A random sample of 200 within each category will be taken and their overall miles per gallon will be measured on a controlled course at different speeds. Discuss the nature of the hypothesis on the basis of the type of data (quantitative or qualitative) that is being analyzed and how the population(s) can be compared.

4. List the five steps required to test a hypothesis of the mean. Be sure that all steps are in the correct sequence.

5. The employees of Jones Construction Co. are allowed a 30-minute lunch break. The owner wants to know if the employees are actually taking 30-minute breaks. The foreman decides to record the times taken for the next 25 breaks taken at the site. The data are as follows:

25 34 28 27 33 40 23 22 26

33 38 25 22 27 30 32 31 24

22 28 32 34 26 24 35

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic.

c. At  = 0.05, should the foreman reject the null hypothesis?

d. What conclusion can the foreman present to the owner?

6. The players on last year's football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team's average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team's progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:

346 412 332 285 396 461 321 275

246 315 298 347 430 419 406 311

319 385 377 365 385 400

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic.

c. At  = 0.01, should Coach Juarez reject the null hypothesis?

d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?

7. Nielsen Media Research reported that in 1998, 70% of the households in the nation owned at least one working television set. Suppose that you conduct a survey of 150 households in your city and discover that 73% of the households owned a working television set. Does your city differ from the rest of the nation?

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic and find the p value.

c. At  = 0.05, do you reject the null hypothesis?

d. What conclusion can you draw?

8. Complete the following table to illustrate your understanding of the hypotheses tests needed to compare two population means:

Two-Sided Test

H0: 1 = 2 or H0:

HA: HA:

Lower-Tail Test

H0: or H0:

HA: 1 < 2 HA:

Upper-Tail Test

H0: or H0:

HA: HA: 1  2 > 0

9. A supermarket chain just added two new stores located on opposite sides of a city. Management is interested in determining if customers are spending an equal time shopping in the stores. The research team temporarily installed a clock punch in each store and asked 100 customers at each location to collect a time card and punch in when they arrived and punch out as they left with their sacks full of groceries. Results from the time cards are summarized in the table below:

Store 1 Store 2

Mean Shopping Time (min.)

Standard Deviation (min.) 89.3

6.6 83.5

7.1

Test the hypothesis that the two means are the same at  = 0.05 versus the alternative hypothesis that the two means are not the same.

10. George Harris is trying to decide between two on-line investment companies to handle his stock transactions. George has decided that he will open an account with the company that can process his transaction requests the fastest. Data measuring the average transaction time for the past 42 days of trading are shown below for each company:

Company 1 Company 2

Mean Transaction Time (min.)

Standard Deviation (min.) 4.35

1.6 4.85

1.1

Test the hypothesis that the two means are the same at  = 0.05 versus the alternative hypothesis that the two means are not the same.

11. A diaper company is considering 3 different filler materials for their disposable diapers. Eight diapers were tested with each of the 3 filler materials and 24 toddlers were randomly given a diaper to wear. As the child played, fluid was injected into to diaper every 10 minutes until the product failed (leaked). The amount of fluid (in grams) at the time of failure was recorded for each diaper. The data are shown below:

Material 1 Material 2 Material 3

791 809 828

789 818 814

796 803 855

802 781 844

810 813 847

790 808 848

800 805 836

790 811 873

a). What is the response variable and what is the factor?

b) How many levels of the factor are being studies?

c) Is there any difference in the amount of fluid the diaper can hold using the 3 different materials? If so, which ones are different?

d) What is your recommendation to the company?

12. Does a heavier bowler knock down more pins? Jim Samuels, manager of Maple Lanes, asked 15 men's league players to report their body weight (lbs) and their league average, rounded to the nearest pin. Results are shown below:

Weight, X Average, Y Weight, X Average, Y

154 156 215 159

159 145 226 152

165 178 237 132

172 201 245 178

178 205 262 196

192 191 280 145

205 187 289 168

211 146

a. Construct a scatter plot of the data

b. Find the equation for the least squares line of best fit

c. Draw the least squares line on the scatter plot

d. Predict the league average for an adult male bowler who weighs 190 lbs.

What can you conclude?

##### Solution Preview

The main things to consider are whether you've got a large sample or small sample, so should you use a z-stat or a t-stat. I used t-stats througout. For hypothesis test you need to know the formula for a t-stat, how to ...

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