A psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown in Table 11.54 . Conduct a test of homogeneity. Test at a 5% level of significance. Given that the p-value = 0.56, what is the decision and reason.

Decision: Do not reject the null hypothesis. Reason for decision: p -value > alpha

Decision: Do not reject the null hypothesis. Reason for decision: p -value < alpha

Decision: reject the null hypothesis. Reason for decision: p -value > alpha

Decision: reject the null hypothesis. Reason for decision: p -value < alpha

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance. Which option shows the null hypothesis?

H 0 : The distribution of fish caught is the same in Green Valley Lake and Echo Lake.

H o : The distribution for fish caught is not the same in Green Valley Lake and in Echo Lake.

H 0 : The distribution of fish caught in Green Valley Lake is proportional to that caught in Echo Lake.

H 0 : The distribution of fish caught in Green Valley Lake is symmetrical to that caught in Echo Lake.

A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance. Which option shows the alternative hypothesis?

Ha : The distribution for fish caught is not the same in Green Valley Lake and in Echo Lake.

H a : The distribution of fish caught is the same in Green Valley Lake and Echo Lake.

H a : The distribution of fish caught in Green Valley Lake is proportional to that caught in Echo Lake.

H a : The distribution of fish caught in Green Valley Lake is symmetrical to that caught in Echo Lake.

Chi-Square test for Homogeneity Quiz

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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 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.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A math teacher wants to see if two of her classes have the same distribution of test scores. What test should she use?

Chi-square test for Homogeneity.

Chi-square test for independence.

The goodness-of-fit test

random test

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

Chi-square Goodness of Fit Test

Chi-Square Test for Homogeneity

Chi-Square Test for Independence/Association

Not a Chi-square test

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.

Chi-square Goodness of Fit Test

Chi-Square Test for Homogeneity

Chi-Square Test for Independence/Association

Not a Chi-square test

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.

Chi-square Goodness of Fit Test

Chi-Square Test for Homogeneity

Chi-Square Test for Independence/Association

Not a Chi-square test

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33.
State the degree of freedom for the distribution

7.

FILL IN THE BLANK QUESTION

1 min • 1 pt

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33.
What is the test statistic? write your answer to 2 decimal places.

8.

FILL IN THE BLANK QUESTION

1 min • 1 pt

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33.
What is the p-value? write your answer to 5 decimal places.

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33.
Which option shows the null hypothesis?

H₀: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.

H₀: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

H₀: The distribution of working hours for private practice doctors is proportional to the distribution of working hours for hospital doctors.

H₀: The distribution of working hours for private practice doctors is skewed just as the distribution of working hours for hospital doctors.

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33.
Which option shows the alternative hypothesis?

H_a: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.

H_a: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

H_a: The distribution of working hours for private practice doctors is proportional to the distribution of working hours for hospital doctors.

H_a: The distribution of working hours for private practice doctors is skewed just as the distribution of working hours for hospital doctors.

Chi-Square test for Homogeneity

20 questions

The p-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion?

A math teacher wants to see if two of her classes have the same distribution of test scores. What test should she use?

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.

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.

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