Nonparametric Statistics (133 problems)

Poll shows that 74% of respondents felt other motorists were driving more aggressively than they did five years ago, 23% felt that other motorists were driving the same way they did 5 years ago, and 3% felt other motorists were driving less aggressively than they were driving 5 years ago. A sample survey of 180 senior drivers found that 125 felt that other motorists were driving more aggressively than they did 5 years ago, 36 felt that other motorists were driving about the same as they did 5 years ago, and 19 felt that other motorists were driving less aggressively than they did 5 years ago. At a significance level of .10 test the claim that senior drivers feel the same way as those who surveyed in the poll. State hypotheses and identify claim, find critical values, compute test value, make decision, summarize results.

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.

For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 400 viewers in the Tampa-St. Petersburg, Florida area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable?

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?

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?

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.

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

Instant oatmeal mix is considering adding flavors to its mix. 200 people tested the flavors and gave preferences. Is there a preference for flavor at the .05 level? State hypotheses and identify claim, find critical value(s) compute test value, make the decision, and summarize results.

Plain 20

Cinnamon 58

Apple 48

Maple 22

Peach 52

Suppose researcher wants to investigate whether proportion of smokers within different age groups is the same. He divides the American population into 4 age groups. Within each age group, he surveys 80 individuals and asks, "have you smoked at lease one cigarette in the past week?". Test at the .01 level. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results. Results of survey are as follows:

A company is considering five possible names for its new product. Before choosing a name, the firm decides to test whether all five names are equally appealing. A random sample of 100 people is chosen, and each person is asked to state his or her choice of the best name among the five possibilities. The numbers of people who chose each one of the names are as follows.

Name: A B C D E

Number of Choices: 4 12 34 40 10

Conduct a chi-square test for goodness of fit and determine whether all five names are equally appealing.

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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A company had 36 absences on Monday, 26 on Tuesday, 10 on Wednesday, 20 on Thursday, and 28 on Friday. At the .05 level, is there a difference in the number of absence per day?

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results.

For the alumni of the graduating classes from the years 1988 to 1991, the following data is available:

Using a 5% level of significance, test the null hypothesis that the percentage of graduates who contributed money is the same across all these graduating classes.

Suppose researcher wants to investigate whether proportion of smokers within different age groups is the same. He divides the American population into 4 age groups. Within each age group, he surveys 80 individuals and asks, "have you smoked at lease one cigarette in the past week?" . Test at the .01 level. State hypotheses and identify claim, find critical value(s), compute test value, make decision, summarize results.

Results of survey are as follows:

Consider the results of a small opinion poll concerning the chances of another stock market crash in the next 12 months comparable to the crash of 1987.

a. Fill in the “Total” row and column.

b. Find the table of overall percentages. Interpret these as estimates of probabilities in the population. In particular, what probabilities do they represent?

c. Find the table of percentages by type of person (stockholder/non-stockholder). Interpret these as estimates of probabilities in the population. In particular, what probabilities do they represent?

d. Find the table of percentages by response. Interpret these as estimates of probabilities in the population. In particular, what probabilities do they represent?

e. Does the response appear to be independent of the stockholder/non-stockholder classification?

f. Find the critical value from the chi-squared table for the 5% level and report the result of the chi-squared test.

g. Find the critical value from the chi-squared table for the 1% level and report the result of the chi-squared test.

h. Find the critical value from the chi-squared table for the 0.1% level and report the result of the chi-squared test.

i. State you conclusions and discuss the results in practical terms.

A survey was conducted asking 200 randomly selected state representatives if they felt their opinions on a bill were related to their party affiliation. The results are shown in the contingency table given below. Test the claim that opinions and party affiliation are independent using the Chi-Square test for independence. Use a = 0.05.

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

Indicate the condition(s) under which you would use a Fisher Exact Test as opposed to the Pearson’s Chi-square test.

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.

Use the given contingency table to (a) find the expected frequencies of each cell in the table, (b) perform a chi-square test for independence, and (c) comment on the relationship between the two variables. Assume the variables are independent. The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use α = 0.01.