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WorksheetsChi square
Total questions: 28
Worksheet time: 3580secs
Name
Class
Date
1.
Find the degrees of freedom.
a)
4
b)
5
c)
6
d)
7
2.
The table shows the number or babies born on each day of the week. Is there evidence that births are more likely on specific days of the week?
a)
yes, the p value is greater than .05
b)
no, the p value is less than .05
c)
yes, the p value is less than .05
d)
no, the p value is greater than .05
3.
Which test would you use to see if the distribution of music that Californians listen to is the same as that of Nevadans? 900 Californians and 600 Nevadans were surveyed.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
4.
Which test would you use .... In 1974, each acre of the Tahoe basin was assessed to see what condition the soil was in. 23% of acres were of type I, 32% were of type II, 41% were of type III, and 16% were of type IV. This year the region was assessed again and the number of each type were again determined.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
5.
Which test would you use to see if gender is a factor choosing a person’s favorite fruit? 900 college students were surveyed and their favorite fruit recorded.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
6.
Which test would you use to see whether the fans that buy tickets are demographically the same as the general population of the city. Currently 42% are Caucasian, 35% are Hispanic, 12% are African American, 8% are Asian, and the rest are defined as other.
a)
Chi-square Goodness of Fit Test
b)
Chi-Square Test for Homogeneity
c)
Chi-Square Test for Independence/Association
d)
Not a Chi-square test
7.
What are the expected counts of a female who likes Pepsi?
a)
10.5
b)
11
c)
14.5
d)
6.3
8.
The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" Here are the data in the table provided. Identify the p-value and decide which of the following is the most appropriate conclusion?
a)
Because 0.0129 is less than α = 0.05, fail to reject H0. There is convincing evidence that the food choices are equally popular.
b)
Because 0.0129 is less than α = 0.05, reject H0. There is convincing evidence that the food choices are not equally popular.
c)
Because 0.0289 is less than α = 0.05, reject H0. There is convincing evidence that the food choices are not equally popular.
d)
Because 0.0289 is less than α = 0.05, fail to reject H0. There is not convincing evidence that the food choices are equally popular.
9.
A chi-square test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The expected counts for spinning a 5 will be
a)
5
b)
10
c)
11.1
d)
20
10.
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 they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are in the table provided. Why hypotheses would be appropriate for performing a chi-square test?
a)
The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.
b)
The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years. The alternative is that the mean is different for at least 2 of the 4 years.
c)
The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university. The alternative is that the distribution is different for at least 2 of the 4 years.
d)
The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.
11.
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 they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are in the table provided. Why hypotheses would be appropriate for performing a chi-square test?
a)
The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.
b)
The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years. The alternative is that the mean is different for at least 2 of the 4 years.
c)
The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university. The alternative is that the distribution is different for at least 2 of the 4 years.
d)
The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.
12.
How do you find the degrees of freedom for a chi-square test of homogeneity?
4 lines
13.
What do you miss the most our in person stats classes?
4 lines
14.
What do you like least about our online classes?
4 lines
15.
What are the degrees of freedom for the following χ² test?
a)
6
b)
2
c)
5
d)
36
16.
What is the expected frequency of a female who likes Pepsi?
a)
10.5
b)
11
c)
14.5
d)
6.3
17.
If the χ2 critical value = 5.99 and the
χ2 calculated value = 7.35, what is the conclusion
a)
Reject Ho
b)
Do not reject Ho
c)
there is not enough info to decide
d)
The conclusion can only be made if we also know the p-value
18.
What statistical model does this graph illustrate?
a)
normal model
b)
t model
c)
chi square model
19.
Which of the following makes for a reasonable null hypothesis for a Chi-Square Goodness of Fit Test?
a)
The distribution of political views this year is 0.24 liberal, 0.38 moderate, 0.38 conservative.
b)
The distribution of political views this year differs from a distribution of 0.24 liberal, 0.38 moderate, 0.38 conservative.
c)
The distribution of political views this year is independent of gender.
d)
This is not a situation where using a Chi-Square Goodness of Fit Test is appropriate.
20.
Given a significance level of 5%, should we accept or reject the null hypothesis.
a)
Since the p-value of 0.231 is greater than the significance level of 0.05, we should accept the null hypothesis.
b)
Since the p-value of 0.447 is greater than the significance level of 0.05, we should accept the null hypothesis.
c)
Since the p-value of 0.231 is less than the significance level of 5%, we should accept the null hypothesis.
d)
Since the p-value of 0.447 is greater than the significance level of 0.05, we should reject the null hypothesis.
21.
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. We compute the value of the χ² statistic to be 6.58. Assuming that the conditions for inference are met, the P-value of our test is
a)
Between 0.10 and 0.20.
b)
Between 0.05 and 0.10.
c)
Between 0.01 and 0.05.
d)
Less than 0.01.
22.
All current-carrying wires produce electro-magnetic (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 is 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 died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC). The data is provided in a table. Which of the following may we conclude, based on the test results?
a)
There is convincing evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.
b)
HCC either causes cancer directly or is a major contributing factor to the development of cancer in children.
c)
There is not convincing evidence of an association between wiring configuration and the type of cancer that cause the deaths of children in the study.
d)
There is convincing evidence that HCC does not cause cancer in children.
23.
All current-carrying wires produce electro-magnetic (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 is 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 died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC). The data is provided in a table. The expected count of cases of lymphoma in the homes with an HCC is
a)
79*31/215
b)
10*21/215
c)
79*31/10
d)
136*31/215
24.
All current-carrying wires produce electro-magnetic (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 is 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 died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC). The data is provided in a table. A Type I error would occur if we found convincing evidence that
a)
HCC wiring caused cancer when it actually didn't.
b)
HCC wiring didn't cause cancer when it actually did.
c)
There is no association between the type of wiring and the form of cancer when there actually is an association.
d)
There is an association between the type of wiring and the form of cancer when there actually is no association.
25.
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. We compute the value of the χ² statistic to be 6.58. Assuming that the conditions for inference are met, the P-value of our test is
a)
Between 0.10 and 0.20.
b)
Between 0.05 and 0.10.
c)
Between 0.01 and 0.05.
d)
Less than 0.01.
26.
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. Assuming H0 is true, the expected number of Hispanic drivers who would receive a ticket is
a)
10.36
b)
11
c)
11.84
d)
12
27.
All current-carrying wires produce electro-magnetic (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 is 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 died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC). The data is provided in a table. The appropriate degrees of freedom for the χ² statistic is
a)
1
b)
2
c)
3
d)
4
28.
All current-carrying wires produce electro-magnetic (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 is 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 died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC). The data is provided in a table. Which of the following may we conclude, based on the test results?
a)
There is convincing evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.
b)
HCC either causes cancer directly or is a major contributing factor to the development of cancer in children.
c)
There is not convincing evidence of an association between wiring configuration and the type of cancer that cause the deaths of children in the study.
d)
There is convincing evidence that HCC does not cause cancer in children.
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