Questions and Answers

The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample?
A) The expected number of blue-collar workers donating to charity is less than 30.
B) The expected number of management workers donating to charity is 100.
C) The expected numbers of other white-collar and blue-collar workers donating to charity are the same.
D) The expected number of other white-collar workers donating to charity is 50.
E) The combined expected numbers of other white-collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.

A reporter intends to survey residents of a city to investigate whether there are differences in use of grocery delivery services by region of the city where the residents live (north, south, west, and east). City residents will be asked to respond yes or no to the question “Do you regularly use a grocery delivery service to purchase groceries?” Results will be collected in a 4-by-2 table of counts organized by region and response to the question. For a chi-square test for homogeneity, which of the conditions listed below is not necessary to investigate whether there are differences between use of grocery delivery service by region?
A) For each cell in the table, (row total)(column total)/table total will be greater than 5.
B) Data should be collected using a stratified random sample, with region as strata.
C) All eight expected cell counts should be greater than 5.
D) The number of residents sampled from each region should be greater than 30.
E) The total number of residents sampled should be at most 10 percent of the total number of residents in the city.

A company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds χ2=0.771 with a corresponding p-value of 0.68. Assuming conditions for inference were met, which of the following is the correct interpretation of the p-value?
A) There is a 68 percent chance of obtaining a chi-square value of at least 0.771.
B) There is a 68 percent chance that the company’s claim is correct.
C) If the null hypothesis were true, there would be a 68 percent chance that the company’s claim is correct.
D) If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of 0.771.
E) If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.

A χ2 goodness-of-fit test proportions was used to test the hypothesis that students at a local university select majors in the same as other universities in the state. A chi-square test statistic of χ2=45.6 was calculated with a corresponding p-value of 0.005. Which of the following is correct?
A) There is sufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
B) There is sufficient evidence to conclude that students at the local university select majors in the same proportions as do students in the rest of the state.
C) There is insufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
D) There is insufficient evidence to conclude that students at the local university select majors in the same proportions as do students in the rest of the state.
E) Students at the local university select majors in the same proportions as do students in the rest of the state.

A chi-square test was conducted to investigate whether there is an association between a person’s favorite flavor of ice cream and their favorite toppings. Each of 200 randomly selected customers at an ice cream parlor was asked to pick their favorite flavor from vanilla, chocolate, chocolate chip, or none of these. They were also asked to pick their favorite topping from chocolate sauce, peanuts, crumbled cookies, crushed candies, or none of these. The hypothesis test had a test statistic of 24.97 with an associated p-value of 0.015. If the significance level of the test was α=0.05, which of the following is the correct decision for this hypothesis test?
A) There is not convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
B) There is convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
C) There is convincing statistical evidence to suggest there is not an association between favorite ice cream flavor and favorite topping.
D) There is proof that a person’s favorite ice cream topping is dependent on the person’s favorite ice cream flavor.
E) There is proof that a person’s favorite ice cream topping is independent of the person’s favorite ice cream flavor.

Which of the following is a reason not to use a chi-square test of homogeneity to analyze a set of data?
A) The data consist of one categorical variable for two or more different populations and are summarized by counts in a two-way table.
B) The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.
C) The data were obtained from more than two populations to investigate whether the proportions for categorical data collected are the same.
D) The data were obtained from four different regions to investigate whether the distribution of a categorical variable is different across the four regions.
E) The data were obtained using a simple random sample of a population from last year and a simple random sample of the same population from this year where the data collected were categorical variables.

If the professionals and the students do not differ in the distributions of their responses, which of the following is equal to the expected number of students who classify the crown shapes as medium?
A) 39
B) ((39)(87))/91
C) ((87)(91))/200
D) ((87)(109))/200
E) ((97)(91))/200

A statistician is conducting a chi-square goodness-of-fit test and is limited by the cost, per individual, to conduct the study. The statistician selects a sample of size 39, which is the smallest sample possible that will meet the condition for large expected counts. Which of the following could not be the null hypothesis for the study?
A) H0: p1=0.20, p2=0.20, p3=0.20, p4=0.20, p5=0.20
B) H0: p1=0.15, p2=0.35, p3=0.22, p4=0.15, p5=0.13
C) H0: p1=0.24, p2=0.23, p3=0.21, p4=0.18, p5=0.14
D) H0: p1=0.34, p2=0.21, p3=0.14, p4=0.15, p5=0.16
E) H0: p1=0.43, p2=0.23, p3=0.17, p4=0.09, p5=0.08

l. H0: p1=p2=p3, where p1 is the proportion of the sample of sophomores that responded yes, p2 is the proportion of the sample of juniors that responded yes, and p3 is the proportion of the sample of seniors that responded yes. ll. H0: There is an association between grade level and whether or not a student regularly recycles plastic bottles. lll. H0: There is no difference in the distribution of regular recyclers across the three grade levels.
A) II only
B) III only
C) I and II only
D) I and III only
E) I, II, and III

The corresponding p-value of 0.03 means that the probability of observing a test statistic of χ2=12.4 is 0.03, assuming the null hypothesis is true. Which of the following is a valid criticism of this interpretation of the p-value?
A) The null hypothesis can never be assumed to be true.
B) The null hypothesis is not stated.
C) The p-value is not the probability of observing 12.4 exactly.
D) The significance level is not stated.
E) The degrees of freedom are not stated.