WorksheetsUnit 8: Chi Square Review
Total questions: 25
Worksheet time: 1hrs 28mins
A chi-square test is used to analyze
the difference in proportions.
The difference between the means of two independent groups.
The distribution of a categorical variable.
The standard deviation of a sample.
Which of the following statements is NOT true about the chi-square statistic?
It is calculated by summing the squared deviations between observed and expected counts, divided by the expected counts.
A larger chi-square value indicates a stronger association between the variables.
The chi-square distribution has a minimum value of zero.
The degrees of freedom for a chi-square test depend on the number of categories in each variable.
In a chi-square goodness of fit test, the null hypothesis states that
The observed and expected frequencies are significantly different.
There is a linear relationship between the two variables.
The proportions of the population fall into specific categories.
The observed data matches the expected distribution.
What is the appropriate test to use with this data?
Chi Square GOF
Chi Square Homogeneity
Chi Square Independence
Chi Square Heterogeneity
Chi-squared GOF test is not appropriate if:
(choose all that apply)
The calculated number is really large
One of the expected values is less than 5
One of the observed values is less than 5
The degrees of freedom = 1
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Computer software was used to analyze the data.
The χ2 statistic is equal to;
(give your answer to 3 decimal places
(a)
The degrees of freedom for the chi-square test for this two-way table are
4
8
10
20
4876
The expected count of females who respond "almost certain" is
487.7
525
965
1038.8
1174
The chi square statistic is
25(18−25)2+...+25(21−25)2
18(25−18)2+...+21(25−21)2
25(18−25)+...+25(21−25)
100(18−25)2+...+100(21−25)2
0.25(0.18−0.25)2+...+0.25(0.39−0.25)2
Find the chi-squared calculated value for the table.
0.486170447
1.442392006
1.45
2
The p-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion?
Because 0.0129 is less than 0.05, reject the null hypothesis. There is not convincing evidence that the food choices are equally popular.
Because 0.0129 is less than 0.05, reject the null hypothesis. There is not convincing evidence that the food choices are equally popular.
Because 0.0129 is less than 0.05, reject the null hypothesis. There is convincing evidence that the food choices are not equally popular.
Because 0.0129 is less than 0.05, we fail to reject the null hypothesis. There is not convincing evidence that the food choices are equally popular.
Because 0.0129 is less than 0.05, fail to reject the null hypothesis. There is convincing evidence that the food choices are equally popular.
Is the religious affiliation distribution among students at a certain university different from the 2020 census?
chi-square test for goodness of fit
chi-square test for independence
chi-square test for homogeneity
t test for regression slope
Is the religious affiliation distribution different between university A and university B?
chi-square test for goodness of fit
chi-square test for independence
chi-square test for homogeneity
t test for regression slope
Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at the current levels. The results are given in the table.
The conditions for carrying out the chi-square test is:
I. Separate random samples from the populations of interest
II. Expected counts large enough
III. The samples themselves and the individual observations in each sample are independent.
Which of the conditions is (are) satisfied in this case?
I only
II only
I and II only
II and III only
I, II and III
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate this, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Data is given in the table.
Computer software was used to analyze the data.
X2 = 0.082 + 0.170 + 0.023 + 0.048 + 0.099 + 0.013 = 0.435
The appropriate count of cases with lymphoma in homes with an HCC is
21579⋅31
21510⋅21
1079⋅31
215136⋅31
None of these
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate this, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Data is given in the table.
Computer software was used to analyze the data.
X2 = 0.082 + 0.170 + 0.023 + 0.048 + 0.099 + 0.013 = 0.435
A Type I error would occur if we conclude that
HCC wiring caused cancer when it actually didn’t.
HCC wiring didn’t cause cancer when it actually did.
There is no association between the type of wiring and the form of cancer when there actually is an association.
There is an association between the type of wiring and the form of cancer when there actually is no association.
The type of wiring and the form of cancer have a positive correlation when they actually don’t.
Which of the following is false?
A chi-square distribution with k degrees of freedom is more right-skewed than a chi-square distribution with k+1 degrees of freedom.
A chi-square distribution never takes negative values
The degrees of freedom for a chi-square test is determined by the sample size
P (X2 > 10) is greater when df = k+1 than when df = k
The area under a chi-square density curve is always equal to 1
When analyzing results from a two-way table, the main distinction between a test for independence and homogeneity is
how the degrees of freedom are calculated.
how the expected counts are calculated.
the number of samples obtained.
the number of rows in the two-way table.
the number of columns in the two-way table.
The shape of the Chi-Square distribution is ___.
Left Skewed
Right Skewed
Unimodal & Symmetric
Bimodal & Symmetric
Which statement is NOT correct about the χ2 test statistic?
a) A value close to 0 would indicate expected counts are much different from observed counts.
b) A large value of the test statistic would be in support of the alternative hypothesis.
c) A small value of the test statistic would indicate evidence supporting the null hypothesis.
A study was conducted to explore the relationship between a child’s birth order and his or her chances of becoming a juvenile delinquent. The subjects were a random sample of girls enrolled in public high schools in a large city. Each subject filled out a questionnaire that measured whether or not she had shown evidence of delinquent behavior, as well as her birth order. The resulting data are given in the table. Conduct a χ2 test of independence between these two variables. Which statement below is true?
The cell with the largest difference between observed and expected counts is “In between/No”
Far more only children in the study had shown evidence of delinquent behavior than we would expect if the null were true.
The relatively high component for the “Oldest/Yes” cell means that the observed count for this cell is considerably higher than the expected count.
