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

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?

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: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 What is the P-value for testing this null hypothesis of a uniform distribution of prescriptions over the 7 days of the week?

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

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?

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?

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

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: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 What is the chi-square statistic for the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week?

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: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 Using a significance level of 0.05, what is the appropriate conclusion for this test?

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?

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: ? ? White 4821 Hispanic 277 African American 510 Asian/Pacific 88 Native American 598 Total 6294 The known ethnic distribution in the United States, according to census data, is as follows: ? ? White 0.756 Hispanic 0.091 Black 0.108 Asian/Pacific 0.038 Native American 0.007 Total 1 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?

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: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 Which of the following is the appropriate null hypothesis for this test?

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: ? Test Contribution Category Observed Proportion Expected to Chi-Sq beer 264 0.333333 216.667 10.3405 wine 237 0.333333 216.667 1.9082 liquor 149 0.333333 216.667 21.1328 N DF Chi-Sq P-Value 650 What are the null hypotheses that correspond to this study's objective?

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: ? ? Test Contribution Category Observed Proportion Expected to Chi-Sq beer 264 0.333333 216.667 10.3405 wine 237 0.333333 216.667 1.9082 liquor 149 0.333333 216.667 21.1328 N DF Chi-Sq P-Value 650 Using a significance level of 5%, what should you conclude?

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 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?

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

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.: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 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 _______________.

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?

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? Test Contribution Category Observed Proportion Expected to Chi-Sq beer 264 0.333333 216.667 10.3405 wine 237 0.333333 216.667 1.9082 liquor 149 0.333333 216.667 21.1328 N DF Chi-Sq P-Value 650

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. Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Prescriptions 42 31 33 29 45 44 21 What can we state about the chi-square test in this situation?