Questions and Answers

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.

Which of the following is closest to the p-value of the appropriate test to investigate whether the proportion of people living in the northern part of the state who are in favor of removing the cash lane is different from the proportion of people living in the southern part of the state who are in favor of removing the cash lane?
A) 0.0671
B) 0.1342
C) 0.5235
D) 0.6912
E) 0.9329

Which of the following is the appropriate test to investigate whether there is an association between opinion about the ballot initiative and highest level of education completed?
A) A two-sample t-test for a difference between means
B) A two-sample z-test for a difference between proportions
C) A chi-square test of homogeneity
D) A chi-square test of independence
E) A chi-square goodness-of-fit test

For which of the following is a chi-square goodness-of-fit test most appropriate?
A) Estimating a difference between two population means
B) Estimating a difference between two population proportions
C) Finding the expected value of a probability distribution
D) Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution
E) Determining the best shape for a set of data

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.

Which of the following is not a condition for a chi-square goodness-of-fit test?
A) Data should be collected using a random sample or randomized experiment.
B) When sampling without replacement, the sample size cannot be greater than 10 percent of the population size.
C) All expected counts should be greater than 5.
D) The distribution of the sample should be approximately normal.
E) During the sampling process, each individual chosen should be independent of the next

The biologist found evidence to reject the null hypothesis in favor of the alternative hypothesis. Which of the following represents the alternative hypothesis of the test?
A) At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked.
B) The proportions for the different fish types are the same as the corresponding proportions when the lake was originally stocked.
C) The proportions are evenly distributed among fish types.
D) At least one of the fish proportions is the same as the corresponding proportion when the lake was stocked.
E) All of the fish proportions are different than the corresponding proportions when the lake was stocked.

If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouses with 1 nest in nongolf locations?
A) 40
B) 42
C) 50
D) 58
E) 60

In order to meet the conditions for independence and large counts for a chi-square goodness-of-fit test, which of the following represents all possible sizes of the monthly samples?
A) n≥30
B) 30≤n≤50
C) 46≤n≤60
D) n≥46
E) n≤60

Assuming that all conditions for inference have been met, which of the following equations gives the appropriate chi-square test statistic and the correct number of degrees of freedom to determine if there is an association between grade level and whether a student approves of the food choices in the cafeteria?
A) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 4 degrees of freedom
B) χ2=(50−35)250+(20−35)220+(30−45)230+(60−45)260 with 4 degrees of freedom
C) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 4 degrees of freedom
D) χ2=(50−40)240+(20−40)240+(30−40)240+(60−40)240 with 1 degree of freedom
E) χ2=(50−35)235+(20−35)235+(30−45)245+(60−45)245 with 1 degree of freedom