Deck 19: The Chi-Square Test for Goodness of Fit

Question 1

Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test:
?
$\begin{array} { l r r r r } & \text { Test } & \text { Contribution } \\ \text { Category } & \text { Observed } & \text { Proportion } & \text { Expected } & \text { to Chi-Sq } \\ \text { beer } & 264 & 0.333333 & 216.667 & 10.3405 \\ \text { wine } & 237 & 0.333333 & 216.667 & 1.9082 \\ \text { liquor } & 149 & 0.333333 & 216.667 & 21.1328 \end{array}$
N DF Chi-Sq P-Value 650 What are the null hypotheses that correspond to this study's objective?

A)H₀: p₁= p₂ = p₃ = 1/3
B)H₀: p₁= 264/650 p₂ = 237/650 p₃ = 149/650
C)H₀: p₁= p₂ = p₃ = 216.667
D)H₀: p₁= 10.34 p₂ = 1.908 p₃ = 21.132

Answer 1

H₀: p₁= p₂ = p₃ = 1/3

Question 2

Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test:
?
?
$\begin{array} { l r r r r } & \text { Test } & \text { Contribution } \\ \text { Category } & \text { Observed } & \text { Proportion } & \text { Expected } & \text { to Chi-Sq } \\ \text { beer } & 264 & 0.333333 & 216.667 & 10.3405 \\ \text { wine } & 237 & 0.333333 & 216.667 & 1.9082 \\ \text { liquor } & 149 & 0.333333 & 216.667 & 21.1328 \end{array}$
N DF Chi-Sq P-Value 650 What is the alternative hypothesis for this test?

A)H_a p₁ = p₂ = p₃= 1/3
B)H_a: p₁ = p₂= p₃ ? 1/3
C)H_a: p₁ ? p₂ ? p₃ ? 1/3
D)H_a: At least one proportion is different

Answer 2

H_a: At least one proportion is different

Question 3

Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test:
?
What is the P-value of this test?
$\begin{array} { l r r r r } & \text { Test } & \text { Contribution } \\ \text { Category } & \text { Observed } & \text { Proportion } & \text { Expected } & \text { to Chi-Sq } \\ \text { beer } & 264 & 0.333333 & 216.667 & 10.3405 \\ \text { wine } & 237 & 0.333333 & 216.667 & 1.9082 \\ \text { liquor } & 149 & 0.333333 & 216.667 & 21.1328 \end{array}$
N DF Chi-Sq P-Value 650

A)Greater than 0.10
B)Less than 0.10 but greater than 0.05
C)Less than 0.05 but greater than 0.01
D)Less than 0.01

Answer 3

Less than 0.01

Question 4

Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test:
?
?
$\begin{array} { l r r r r } & \text { Test } & \text { Contribution } \\ \text { Category } & \text { Observed } & \text { Proportion } & \text { Expected } & \text { to Chi-Sq } \\ \text { beer } & 264 & 0.333333 & 216.667 & 10.3405 \\ \text { wine } & 237 & 0.333333 & 216.667 & 1.9082 \\ \text { liquor } & 149 & 0.333333 & 216.667 & 21.1328 \end{array}$
N DF Chi-Sq P-Value 650 Using a significance level of 5%, what should you conclude?

A)There are significantly more American adult drinkers who favor beer over wine or liquor.
B)There is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often.
C)The data are consistent with an equal distribution of beer, wine, and liquor as the alcoholic drink consumed most often by American adults who drink alcohol.
D)We are unable to conclude anything, because the test assumptions are not met.

Question 5

Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:
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$$\begin{array} { | l | r | } \hline \text { White } & 4821 \\\hline \text { Hispanic } & 277 \\\hline \text { African American } & 510 \\\hline \text { Asian/Pacific } & 88 \\\hline \text { Native American } & 598 \\\hline \text { Total } & 6294 \\\hline\end{array}$$ The known ethnic distribution in the United States, according to census data, is as follows:
?
$$\begin{array} { | l | l | } \hline \text { White } & 0.756 \\\hline \text { Hispanic } & 0.091 \\\hline \text { Black } & 0.108 \\\hline \text { Asian/Pacific } & 0.038 \\\hline \text { Native American } & 0.007 \\\hline \text { Total } & 1 \\\hline\end{array}$$ We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. What does the null hypothesis for this test state?

A)All five counts are equal.
B)All five sample proportions are equal.
C)All five population proportions are equal.
D)All five population proportions are equal to their respective U.S.census proportions.

Question 6

Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:
?
?
$$\begin{array} { | l | r | } \hline \text { White } & 4821 \\\hline \text { Hispanic } & 277 \\\hline \text { African American } & 510 \\\hline \text { Asian/Pacific } & 88 \\\hline \text { Native American } & 598 \\\hline \text { Total } & 6294 \\\hline\end{array}$$ The known ethnic distribution in the United States, according to census data, is as follows:
?
?
$$\begin{array} { | l | l | } \hline \text { White } & 0.756 \\\hline \text { Hispanic } & 0.091 \\\hline \text { Black } & 0.108 \\\hline \text { Asian/Pacific } & 0.038 \\\hline \text { Native American } & 0.007 \\\hline \text { Total } & 1 \\\hline\end{array}$$ We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. What is the expected count of Hispanics under the null hypothesis?

A)277
B)25.207
C)572.754
D)152.72

Question 7

Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:
?
?
$$\begin{array} { | l | r | } \hline \text { White } & 4821 \\\hline \text { Hispanic } & 277 \\\hline \text { African American } & 510 \\\hline \text { Asian/Pacific } & 88 \\\hline \text { Native American } & 598 \\\hline \text { Total } & 6294 \\\hline\end{array}$$ The known ethnic distribution in the United States, according to census data, is as follows:
?
?
$$\begin{array} { | l | l | } \hline \text { White } & 0.756 \\\hline \text { Hispanic } & 0.091 \\\hline \text { Black } & 0.108 \\\hline \text { Asian/Pacific } & 0.038 \\\hline \text { Native American } & 0.007 \\\hline \text { Total } & 1 \\\hline\end{array}$$ We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. Software gives a chi-square statistic ?² = 7256.21 for these data. What is the P-value for this test?

A)Greater than 0.05
B)Less than 0.05 but greater than 0.01
C)Less than 0.01 but greater than 0.001
D)Less than 0.001

Question 8

Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:
?
?
$$\begin{array} { | l | r | } \hline \text { White } & 4821 \\\hline \text { Hispanic } & 277 \\\hline \text { African American } & 510 \\\hline \text { Asian/Pacific } & 88 \\\hline \text { Native American } & 598 \\\hline \text { Total } & 6294 \\\hline\end{array}$$ The known ethnic distribution in the United States, according to census data, is as follows:
?
?
$$\begin{array} { | l | l | } \hline \text { White } & 0.756 \\\hline \text { Hispanic } & 0.091 \\\hline \text { Black } & 0.108 \\\hline \text { Asian/Pacific } & 0.038 \\\hline \text { Native American } & 0.007 \\\hline \text { Total } & 1 \\\hline\end{array}$$ We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. At significance level alpha = 1%, what should you conclude?

A)There is significant evidence that the population studied does not match the ethnic composition of the U.S. population.
B)The data are consistent with a uniform distribution of ethnicities.
C)The data prove that the population studied matches the ethnic composition of the U.S. population.
D)We are unable to conclude anything because the test assumptions are not met.

Question 9

Given that a goodness-of-fit test has the null hypothesis rejected, what is the next step in investigating the distribution?

A)Compare the observed and expected percentages.
B)Compare the observed and expected cell counts.
C)Look for the larger components of the chi-square statistic.
D)All of the above

Question 10

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. What is the null hypothesis for the phycologist's test?

A)H₀: p₁= p₂ = p₃ = 1/3
B)H₀: p₁= 1/15, p₂ = 1/25, p₃ = 1/10
C)H₀: p₁ = 15/60, p₂ = 25/60, p₃ = 10/60
D)Impossible to determine from the given information

Question 11

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. What is the alternative hypothesis for the phycologist's test?

A)H_a p₁ = p₂ = p₃= 1/3
B)H_a: p₁ = p₂= p₃ ≠ 1/3
C)H_a: p₁ ≠ p₂ ≠ p₃ ≠ 1/3
D)H_a: At least one proportion is different

Question 12

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. Under the null hypothesis of a uniform distribution of algae to phyla, what is the expected number of algae samples that would be categorized as Chlorophyta?

A)10
B)15
C)20
D)25

Question 13

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. Under the null hypothesis of a uniform distribution of algae to phyla, what is the chi-square component due to Heterokontophyta?

A)-5.00
B)-1.25
C)1.25
D)5.00

Question 14

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. What is the chi-square statistic for the phycologist's test?

A)0
B)7.50
C)20
D)150

Question 15

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. When determining the significance of the chi-square statistic, how many degrees of freedom should the phycologist use?

A)1 degree of freedom
B)2 degrees of freedom
C)3 degrees of freedom
D)4 degrees of freedom

Question 16

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyla, and he believes the phyla should be uniformly distributed. A simple random sample of 60 alga was obtained, and each was categorized as being a member of Rhodophyta, Chlorophyta, or Heterokontophyta. The observed counts were 25, 25, and 10, respectively. What is the p-value of the chi-square statistic in this case?

A)Greater than 0.10
B)Less than 0.10 but greater than 0.05
C)Less than 0.05 but greater than 0.01
D)Less than 0.01

Question 17

A study finds that a simple random sample of 57 butterflies captured in a given natural habitat is made up of 12 blue, 19 yellow, and 26 white butterflies. We want to know if this is significant evidence that blue, yellow, and white butterflies are not equally represented in the habitat's population of butterflies. Under the null hypothesis of equal representation of the three butterfly colors, what is the expected count for blue butterflies?

A)10
B)12
C)19
D)28.5

Question 18

A study finds that a simple random sample of 57 butterflies captured in a given natural habitat is made up of 12 blue, 19 yellow, and 26 white butterflies. We want to know if this is significant evidence that blue, yellow, and white butterflies are not equally represented in the habitat's population of butterflies. What is the value of the chi-square statistic for this test, approximately?

A)0.08
B)0.33
C)2.57
D)5.16

Question 19

A study finds that a simple random sample of 57 butterflies captured in a given natural habitat is made up of 12 blue, 19 yellow, and 26 white butterflies. We want to know if this is significant evidence that blue, yellow, and white butterflies are not equally represented in the habitat's population of butterflies. What is the P-value of this test?

A)Greater than 0.10
B)Less than 0.10 but greater than 0.05
C)Less than 0.05 but greater than 0.01
D)Less than 0.01

Question 20

A study finds that a simple random sample of 57 butterflies captured in a given natural habitat is made up of 12 blue, 19 yellow, and 26 white butterflies. We want to know if this is significant evidence that blue, yellow, and white butterflies are not equally represented in the habitat's population of butterflies. Using appropriate technology at significance level alpha = 5%, what should you conclude?

A)There is significant evidence that the three butterfly colors are not equally represented in that habitat.
B)The data are consistent with an equal representation of the three butterfly colors in that habitat.
C)The data prove that the three butterfly colors are equally represented in that habitat.
D)We are unable to conclude anything because the test assumptions are not met.

Question 21

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows:
$$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } & \text { Saturday } & \text { Sunday } \\\hline \text { Prescriptions } & 42 & 31 & 33 & 29 & 45 & 44 & 21 \\\hline\end{array}$$ Which of the following is the appropriate null hypothesis for this test?

A)H₀: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇ = 1/7
B)H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 5/7 and p₆ = p₇ = 2/7
C)H₀: p₁ = 0.17, p₂ = 0.13, p₃ = 0.13, p₄ = 0.12, p₅ = 0.18, p₆ = 0.18, p₇ = 0.09
D)None of the above

Question 22

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows:
Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the expected count of prescriptions for Monday is _________________.

Question 23

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows.:
Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the chi-square contribution for Monday is _________________.

Question 24

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows.:
To test this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the degrees of freedom for the chi-square test is _______________.

Question 25

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows:
$$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } & \text { Saturday } & \text { Sunday } \\\hline \text { Prescriptions } & 42 & 31 & 33 & 29 & 45 & 44 & 21 \\\hline\end{array}$$ What is the chi-square statistic for the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week?

A)1/7
B)3.5
C)13.8
D)24.5

Question 26

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a random sample of 245 prescription receipts and finds that they are distributed as follows:
$$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } & \text { Saturday } & \text { Sunday } \\\hline \text { Prescriptions } & 42 & 31 & 33 & 29 & 45 & 44 & 21 \\\hline\end{array}$$ What is the P-value for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week?

A)Greater than 0.10
B)Less than 0.10 but greater than 0.05
C)Less than 0.05 but greater than 0.01
D)Less than 0.01

Question 27

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows:
$$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } & \text { Saturday } & \text { Sunday } \\\hline \text { Prescriptions } & 42 & 31 & 33 & 29 & 45 & 44 & 21 \\\hline\end{array}$$ Using a significance level of 0.05, what is the appropriate conclusion for this test?

A)All 7 days of the week have different prescription rates.
B)There is significant evidence that prescriptions are not uniformly distributed over the 7 days of the week.
C)Weekdays and weekends have significantly different prescription rates.
D)The data are consistent with prescriptions being uniformly distributed over the 7 days of the week.

Question 28

The manager of a pharmacy wants to know if prescriptions are filled uniformly over the 7 days of the week. The manager takes a simple random sample of 245 prescription receipts and finds that they are distributed as follows.
$$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } & \text { Thursday } & \text { Friday } & \text { Saturday } & \text { Sunday } \\\hline \text { Prescriptions } & 42 & 31 & 33 & 29 & 45 & 44 & 21 \\\hline\end{array}$$ What can we state about the chi-square test in this situation?

A)The test is valid because the sample size is large.
B)The test is valid because the sample is random and the observed counts are large enough.
C)The test is valid because the sample is random and the expected counts are large enough.
D)The test is not valid because we do not know the true population proportions.

Question 29

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? Which of the following is the appropriate null hypothesis for this test?

A)H₀: p_Current ≠ p_Former ≠ p_Never
B)H₀: p_Current = 0.55, p_Former = 0.22, p_Never = 0.23
C)H₀: p_Current = p_Former = p_Never = 1/3
D)None of the above

Question 30

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? Under the null hypothesis of an equal representation of current, former, and never smokers among adults diagnosed with gum disease, what is the expected count of current smokers?

A)1/3
B)55
C)742
D)1349.33

Question 31

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? What is the chi-square statistic for the null hypothesis of an equal representation of current, former, and never smokers among adults diagnosed with gum disease?

A)1/3
B)854.95
C)1349.33
D)4048

Question 32

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? To test this null hypothesis of an equal representation of current, former, and never smokers among adults diagnosed with gum disease, how many degrees of freedom is associated with the chi-square statistic?

A)1
B)2
C)3
D)4

Question 33

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? What is the P-value for testing this null hypothesis of an equal representation of current, former, and never smokers among adults diagnosed with gum disease?

A)Greater than 0.10
B)Less than 0.10 but greater than 0.05
C)Less than 0.05 but greater than 0.01
D)Less than 0.01

Question 34

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? Using a significance level of 0.05, what is the appropriate conclusion for this test?

A)There is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.
B)Current smokers make up a significantly greater proportion of adults diagnosed with gum disease than former or never smokers.
C)Current smokers are most likely to have gum disease.
D)The data are consistent with an equal representation of current, former, and never smokers among adults diagnosed with gum disease.

Question 35

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is, Do these data indicate that gum disease is equally likely regardless of smoking status? Is the chi-square test valid in this situation?

A)No, because the study is not a randomized experiment.
B)Yes, because the sample size is large.
C)Yes, because the sample is random and the observed counts are large enough.
D)Yes, because the sample is random and the expected counts are large enough.

Question 36

Which of the following is NOT a requirement for the validity of the chi-square goodness-of-fit test?

A)Independent observations
B)A fixed number of observations
C)All observations falling into one of k outcome classes
D)Normally distributed data

Question 37

An experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. We want to know if these data are consistent with Mendel's hypothesis. Which of the following statistical inference procedures should we use?

A)Chi-square test for goodness of fit
B)Chi-square test for two-way table
C)Two-sample t test
D)One-sample t test

Question 38

Which of the following statements about a chi-square hypothesis test is true?

A)When observed counts are far from expected counts, we have evidence against H₀.
B)Large values of x² indicate evidence against H₀.
C)Expected counts are hypothetical, and do not have to be whole numbers.
D)All of the above

Question 39

The P-value of the chi-square test is the area to the left of the calculated C² statistic under this chi-square distribution.

Question 40

Under which of the following conditions can a large P- value arise?

A)H₀ is indeed true.
B)H₀ is not actually true, but too close to the real population distribution for us to tell them apart statistically.
C)H₀ is definitely not true, but the sample size is too small or the variability is too great to reach significance.
D)All of the above