Chi-Square test for Homogeneity

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.

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

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

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

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.

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.

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.