Questions and Answers

A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was χ2=8.2. Which of the following represents the p-value for the test?
A) P(χ2≥8.2)=0.08
B) P(χ2≥8.2)=0.04
C) P(χ2≤8.2)=0.96
D) P(χ2=8.2)=0.00
E) The p-value cannot be calculated because the sample size is not given.

A large factory that builds machines has three shifts, one that starts at 4:00 A.M., one that starts at noon, and one that starts at 8:00 P.M. The manager of the factory wanted to know whether there is an association between an employee’s work experience (less than five years with the company, between five and twenty years with the company, over twenty years with the company) and the time of the employee’s shift. The manager selected a random sample of 125 employees and classified employees by their shift time and work experience. Which of the following is an appropriate pair of hypotheses for the manager to use?
A) H0 : Work experience is independent of the time of an employee’s shift.
Ha : Work experience is dependent on the time of an employee’s shift.
B) H0 : Employees with over 20 years of experience are just as likely to start work at 8 P.M.
Ha : Employees with over 20 years of experience are less likely to start work at 8 P.M.
C) H0 : There is an association between work experience and an employee’s shift.
Ha : There is no association between work experience and an employee’s shift.
D) H0 : For each shift, there is no difference between the proportions of work experience level.
Ha : For each shift, there is a difference between the proportions of work experience level.
E) H0 : Among those in the sample, the proportion of employees for each work experience level did not differ by shift.
Ha : Among those in the sample, the proportion of employees for each work experience level did differ by shift.

The logging company would like to use its sample to provide convincing statistical evidence that over 50 percent of the trees in the forest are spruce trees. The logging company has decided to use a chi-square goodness-of-fit test to justify its claim. Why is the chi-square goodness-of-fit test not an appropriate procedure for the logging company to use?
A) A chi-square goodness-of-fit test would be used to show that the entire distribution of trees in the forest is different than what the forester reported, not necessarily the individual proportion representing the spruce trees.
B) The logging company should find the average number of spruce trees using several samples and then construct a confidence interval for a difference in population means to show that there are more spruce trees in the forest than reported.
C) The logging company does not need to complete an inference procedure; there are more than 50 percent spruce trees in the sample.
D) In order to perform a chi-square test, the logging company needs expected counts, not percentages. The logging company should declare its current sample as expected values and then generate a new sample of observed values to compute the test statistic.
E) The sample does not meet the minimum requirements needed for a chi-square goodness-of-fit test.

A survey was conducted to investigate whether there is an association between a person’s age and their thoughts on what a state senate should do about state parks. Participants selected from “leave state parks the way they are,” “increase funding to state parks,” or “completely overhaul state parks,” and their age was categorized as under 30 years old, between 30 and 50 years old, and over 50 years old. The hypothesis test statistic was calculated to be 15.01. Which of the following is closest to the p-value of the test?
A) 0.0047
B) 0.0103
C) 0.0202
D) 0.9897
E) 0.9953

Which of the following chi-square distributions has the smallest number of degrees of freedom? (graph)

A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?
A) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller.
B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
C) Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
D) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same.
E) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.

How are the expected counts calculated when a chi-square goodness-of-fit test is conducted?
A) The expected counts are calculated by multiplying each proportion in the null hypothesis by 100.
B) The expected counts are calculated by multiplying each proportion in the alternative hypothesis by 100.
C) The values observed from the sample are the expected counts.
D) The expected counts are calculated by multiplying each proportion in the null hypothesis by the sample size.
E) The expected counts are calculated by multiplying each proportion in the alternative hypothesis by the sample size.

An administrator at a local high school wants to investigate whether there is an association between the grade level of a student (either ninth, tenth, eleventh, or twelfth) and how the student commutes to school (either walks, bikes, takes the bus, receives a ride, or drives). After a chi-square test for association was conducted, the results indicated that the chi-square test statistic was 14.63 with a p-value of 0.2623. Which of the following is the correct interpretation of the p-value in the context of the test?
A) There is a 26.23 percent chance that grade level and how a student commutes to school are independent.
B) There is a 26.23 percent chance that there is no association between grade level and how a student commutes to school.
C) Assuming there is no association between a student’s grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.
D) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.
E) Assuming that a student’s grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or smaller

If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?
A) 40
B) 42
C) 50
D) 58
E) 60

Which of the following is true about the chi-square test for homogeneity?
A) The number of subjects randomly assigned to each treatment is not the same; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
B) Volunteers do not constitute a random sample from the population of all patients with the chronic intestinal condition; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
C) Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
D) Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test of homogeneity.
E) Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for homogeneity.