Exam 12: Tests of Goodness of Fit, Independence, and Multiple Proportions

The number of categories of outcomes per trial for a multinomial probability distribution is _____.

In order NOT to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be _____.

An important application of the chi-square distribution is _____.

The properties of a multinomial experiment include all of the following EXCEPT _____.

The sampling distribution for a goodness of fit test is the _____.

Excel's CHISQ.DIST function can be used to perform _____.

Shown below is a 2 × 3 contingency table with observed values from a random sample of size 500. At 95% confidence, test for independence of the row and column factors. Column Factor Row Factor x y z A 40 50 110 B 60 100 140

The degrees of freedom for a contingency table with 6 rows and 3 columns is _____.

Before the rush began for Christmas shopping, a department store noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush, a random sample of 150 shoppers was selected. Of those, 46 used the store's credit card, 43 used a major credit card, and 61 paid cash. Use α = .05 to determine if the methods of payment have changed during the Christmas rush.

Dr. Ross's diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where a random sample of individuals took part in a placebo controlled study. ​ Diet Pills No Diet Pills Total No Weight Loss 80 20 100 Weight Loss 100 100 200 Total 180 120 300 ​ With 95% confidence, determine if weight loss is dependent upon taking the diet pills.

Shown below is a 3 × 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors. Column Factor Row Factor x y Total A 450 300 750 B 300 300 600 C 150 0 150 Total 900 600 1,500

A random sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. The results of the survey are shown below. Income Category Male Female Category 1: \ 20,000 up to \ 40,000 10 30 Category 2: \ 40,000 up to \ 60,000 35 15 Category 3: \ 60,000 up to \ 80,000 15 45 Test at α = .05 to determine if the yearly income is independent of the gender.

Employee panel preferences for three proposed company logo designs follow. ? Design A Design B Design C 78 59 66 ? Use $\alpha$ = .05 and test to determine any difference in preference among the three logo designs.

A population where each element of the population is assigned to one and only one of several classes or categories is a _____.

City planners are evaluating three proposed alternatives for relieving the growing traffic congestion on a north-south highway in a booming city. The proposed alternatives are: (1) designate high-occupancy vehicle (HOV) lanes on the existing highway, (2) construct a new, parallel highway, and (3) construct a light (passenger) rail system. In an analysis of the three proposals, a citizen group has raised the question of whether preferences for the three alternatives differ among residents near the highway and nonresidents. A test of independence will address this question, with the hypotheses being: H₀: Proposal preference is independent of the residency status of the individual H_a: Proposal preference is not independent of the residency status of the individual A simple random sample of 500 individuals has been selected. A crosstabulation of the residency statuses and proposal preferences of the individuals sampled is shown below. PROPOSAL RESIDENCY STATUS HOV Lanes New Highway Light Rail Nearby Resident 110 45 70 Distant Resident 140 75 60 Conduct a test of independence using α = .05 to address the question of whether residency status is independent of the proposal preference.

Excel's ____ function is used to perform a goodness of fit test.

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is _____.