Inference for Categorical Data

AP Statistics

Inference for Categorical Data

1. Most computer software companies provide a telephone number that customers can use to obtain technical assistance. A particular manufacturer recently changed from a toll number to a free 800 number. The distribution for the lengths of calls (in seconds) when the number was a toll call is given below. (state the hypothesis, list the expected distribution, run the test, state the (approximate) p-value, draw your conclusion)

After installing the 800 number, a random sample of 300 calls had the following durations.

Is there sufficient evidence to conclude that a change has occurred in the distribution of the lengths of calls now that the number is toll free? Test at the 0.02 level.

1. The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of Red Lake (Northwest Territories) are shown below (based on U.S. Bureau of the Census, International Data Base). Ages are in years.

Age / % of Canadian Population / Observed Number in Red Lake Village
Under 5 / 7.2% / 47
5 to 14 / 13.6% / 75
15 to 64 / 67.1% / 288
65 and older / 12.1% / 45

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of Red Lake Village.

1. Holly Roller often gets bored while baby-sitting Ima’s children who live next door. Now, Ms. Gambler likes to have her children play board games instead of video games, so Holly has access to numerous 6-sided dice. Holly has kept track of the results of 200 rolls while baby-sitting Ima’s children. The results are displayed below.

Is there reason to believe the die Holly is rolling is not fair?

1. A study compared noncombat mortality rates for U.S. military personnel who were deployed in combat situations to those not deployed. The results of a random sample of 1580 military personnel:

Cause of Death

Unintentional Injury / Illness / Homicide or Suicide

Deployed

/ 183 / 30 / 11
Not deployed / 784 / 264 / 308

At the 0.05 significance level, test the claim that the cause of a noncombat death is independent of whether the military person was deployed in a combat zone.

1. The article “Factors Associated with Sexual Risk-Taking Behaviors Among Adolescents” (J. Marriage and Family ,1994) examined the relationship between gender and contraceptive use by sexually active teens. Each person in a random sample of sexually active teens was classified according to gender and contraceptive use. The data is presented below:

Gender

Contraceptive Use / Female / Male
Rarely/Never / 210 / 350
Sometimes/Most Times / 190 / 320
Always / 400 / 530

We are interested in determine whether there is an association between gender and contraceptive.

1. The numberis an irrational number with the property that when we try to express it in decimal form, it requires an infinite number of decimal places and there is no pattern of repetition. In the decimal representation of, the first 100 digits occur with the frequencies described in the table below. At the 10% significance level, test the claim that the digits are uniformly distributed.

1. In the past, a number of professions were prohibited from advertising. In 1977, the U.S. Supreme Court ruled that prohibiting doctors and lawyers from advertising violated their right to free speech. The article “Should Dentists Advertise?” compared the attitudes of consumers and dentists toward the advertising of dental services. Separate random samples of 101 consumers and 124 dentists were asked to respond to the following statement “I favor the use of advertising by dentists to attract new patients.” The data is presented below:

Strongly Agree / Agree / Neutral / Disagree / Strongly Disagree

Consumers

/ 34 / 49 / 9 / 4 / 5
Dentists / 9 / 18 / 23 / 28 / 46

The authors of the article were interested in determining whether the two groups differed in their attitudes toward advertising.