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

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 Under the null hypothesis of a uniform distribution of prescriptions over the 7 days of the week, the chi-square contribution for Monday is _________________.

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?

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

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?

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. What is the expected count of Hispanics under the null hypothesis?

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 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?

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 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?

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. What does the null hypothesis for this test state?

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?

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

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. At significance level alpha = 1%, what should you conclude?

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?

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 is the alternative hypothesis 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? Is the chi-square test valid in this situation?

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 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 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?