FOR THESE PROBLEMS, PERFORM THESE STEPS:

1. state hypotheses, identify claim
2. find critical value
3. compute test value
4. make the decision
5. Summarize the results

Use the traditional method of hypothesis testing unless otherwise specified.

5.         Staff member wishes to determine whether the number of accidents is equally distributed during the week. A week was selected at random, and following data were obtained. Is there evidence to reject the hypothesis that the number of accidents is equally distributed throughout the week, at a = 0.05?

9. A poll asked adults whether they felt genetically modified food was safe to eat. 35% felt it was safe, 52% felt it was not safe, and 13% had no opinion.  Random sample of 120 adults was asked the same question at a fair. 40 people felt that genetically modified food was safe, 60 felt that it was not safe, and 20 had no opinion. At the 0.01 level of significance, is there sufficient evidence to conclude that the proportions differ from those reported in the survey?

13.       Article states that 53% of adult shoppers prefer to pay cash for purchases, 30% use checks, 16% use credit cards, and 1% have no preference. Store randomly selected 800 shoppers and asked their payment preferences. Results were that 400 paid cash, 210 paid by check, 170 paid with credit card, 20 had no preference. AT a=0.01, test the claim that the owner’s customers have the same preferences as those surveyed.

15.       Populations of state prisons nationwide by serious offenses are the following: violent offenses, 29.5%; property offenses, 29%; drug offenses, 30.2%; public order offenses-weapons, 10.6%; other, 0.7%. A state prison official wants to check how this compares to her state. She surveys 1000 inmates and finds 298 are violent offenders, 275 are property offenders, 344 are drug offenders, 80 are public order offenders, and 3 have other offenses. Can she conclude that the percentages for her prison are the same as national statistics? Use a=0.05.

17.       Manager believes that 50% of her customers purchase word processing programs, 25% purchase spreadsheet programs, and 25% purchase database programming. A sample of purchases shows the following distribution. At a=0.05, is her assumption correct?  Use the P-value method.

Program              word processing                    spreadsheet                database

No. of

Purchases 38                                            23                                19

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11-3   FOR THESE PROBLEMS PEFORM THESE STEPS:

1. state hypotheses and identify claim
2. find critical value
3. compute the test value
4. Make the decision
5. Summarize the results

Use traditional method of hypothesis testing unless otherwise specified.

9.         Is the type of pet owned dependent on annual household income? Use a=0.05.

13.       Some 300 men and 210 women were asked about how many ads in all media they think they saw or heard during one day. The results are shown:

At a=0.01, is the number of ads people feel that they see or hear related to the gender of the person?

15.       Researcher who wants to see if there is a relationship between working and grades collects the following data:

With a = 0.05, can the researcher claim working and grades are independent?

19.       Survey at park shows this selection of snacks purchased. At a=0.10, is the snack chosen independent of the gender of the consumer?

23.       According to survey, 64% of Americans between ages of 6 and 17 cannot pass a basic fitness test. A PE instructor wishes to determine if percentages of such students in different schools in his school district are the same.  He administers a basic fitness test to 120 students in each of 4 schools. The results are shown here. At a=0.05, test the claim that the proportions who pass the test are equal.

27.       Researcher surveyed 100 randomly selected lawyers in each of 4 areas of the country and asked them if they had performed pro bono work for 25 or fewer hours in the last year. The results are shown here. At a=.10, is there enough evidence to reject the claim that the proportions of those who accepted pro bono work for 25 hours of less are the same in each area?

29.       Children’s playground equipment manufacturer read in survey that 55% of all US playground injuries occur on the monkey bars. The manufacturer wishes to investigate playground injuries in 4 different parts of the country to determine if proportions of accidents on the monkey bars are equal. Results are shown here. At a=.05, test the claim that the proportions are equal. Use the P-value method.

31.       President of supermarket wished to determine if customers made a list before going shopping. She surveyed 288 customers in 3 stores. Results are shown here.  At a=0.10, test the claim that the proportions of the customers in the 3 stores who made a list before going shopping are equal.

If the null hypothesis is rejected in these problems, use the Scheffe 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.  Assume that all variables are normally distributed, that the samples are independent, and that the population variances are equal.  Also for each problem, perform the following steps:

1. state hypotheses and identify the claim
2. find the critical value
3. compute the test value
4. make the decision
5. summarize the results, and explain where the differences in the means are.

9.         Number of grams of fiber per serving for a random sample of 3 different kinds of foods is listed. It there sufficient evidence at the 0.05 level of significance to conclude that there is a difference in mean fiber content among breakfast cereals, fruits, and vegetable?

11.       Lengths (in feet) of a random sample of suspension bridges in the US, Europe, and Asia are shown. At a=.05, is there sufficient evidence to conclude that there is a difference in mean lengths?

15.       Numbers (in thousands) of farms per state found in 3 sections of the country are listed below. Test the claim at a=.05 that the mean number of farms is the same across these 3 geographic divisions.

For these problems assume that all variable are normally or approximately normally distributed, that the samples are independent and that the population variances are equal.

1. state hypotheses
2. find critical value for each F test
3. complete the summary table and find the test value.
4. make the decision
5. summarize the results. Draw a graph of the cell means if necessary.

11.       A medical researcher wishes to test the effects of 2 diets and the time of day on the sodium level in person’s blood.  Eight people are randomly selected, and two are randomly assigned to each of the four groups. Analyze the data shown in the tables here, using a two-way ANOVA at a=0.05.  The sodium content is measured in milliequivalents per liter.

Diet Type       I                                               II

Time

8:00 am                       135        145                            138        141

8:00 PM                      155         162                           171         191

13.       Two programs in outdoor survival are available for army recruits. One lasts one week and the other lasts 2 weeks. The officer wishes to test the effectiveness of the programs and see whether there are any gender differences. Six subjects are randomly assigned to each of the programs according to gender. After completing the program, each is given a written test on his or her knowledge of survival skills. The test consists of 100 questions. The scores of the groups are shown here. Use a=0.10 and analyze the data, using a two-ways ANOVA.

DURATION

One Week                              Two Weeks

GENDER

Female 86, 92, 87, 88, 78, 95              78, 62, 56, 54, 65, 63

Male 52, 67, 53, 42, 68, 71              85, 94, 82, 84, 78, 91

15.       A company sells 3 items: swimming pools, spas, saunas. Owner decides to see whether age of the sales rep and the type of item affect monthly sales. At a=0.05, analyze the data shown, using a two-way ANOVA. Sales are given in hundreds of dollars for a randomly selected month, and five salespeople were selected for each group.

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