Exam 9: Comparing More Than Two Proportions

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Fill in the table below with the expected counts based on the hypothesized model that people are equally likely to be born on any day of the seven days of the week.

As the chi-square statistic increases, the p-value increases.

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -Use the Multiple Proportions applet to calculate an approximate p-value for this test. Use at least 1,000 shuffles.

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Use the Goodness of Fit applet to conduct a simulation-based chi-square goodness-of-fit test using the MAD (mean absolute difference) statistic, and report the statistic and the p-value. Use at least 1000 shuffles. MAD statistic = p-value =

According to the 2019 U.S. Census Bureau estimates, 63.4% of the U.S. self-identifies as Non-Hispanic white, 15.3% as Hispanic and Latino, 13.4% as Black or African American, 5.9% as Asian, and 2.0% as Other. A random sample of 1000 students graduating from California colleges and universities resulted in the following data on self-identified race: You would like to determine if the distribution of self-identified race among California college and university students differs from the distribution of self-identified race in the U.S. overall. -What is the expected count based on the null model for the "Hispanic or Latino" cell?

According to the 2019 U.S. Census Bureau estimates, 63.4% of the U.S. self-identifies as Non-Hispanic white, 15.3% as Hispanic and Latino, 13.4% as Black or African American, 5.9% as Asian, and 2.0% as Other. A random sample of 1000 students graduating from California colleges and universities resulted in the following data on self-identified race: You would like to determine if the distribution of self-identified race among California college and university students differs from the distribution of self-identified race in the U.S. overall. -Are the validity conditions met for a theory-based chi-square goodness-of-fit test?

Why do we do overall tests when comparing multiple proportions and not just do the follow-up confidence intervals?

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Based upon a p-value of 0.53, what is the appropriate conclusion for the test?

Hope student researchers want to determine if students yawning (when being yawned at) is asso-ciated with the time of day (morning, afternoon, and evening). They found the following results when they yawned in front of people around campus: • Morning: 25 of the 39 people yawned • Afternoon: 15 of the 38 people yawned • Evening: 29 of the 44 people yawned -Fill in the following two-way table with the observed data.

Is there an association between a person's political affiliation (Democrat, Republican, or Inde-pendent) and whether or not they give to charity? -Describe the appropriate parameter(s) and assign symbols(s) to the parameters. Select all that apply

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -What is the null hypothesis to determine if there is an association between BMI and if a person browses first?

As the Mean Group Diff statistic increases, the p-value decreases.

Suppose three students were interested in studying the association between a person's political party (Democrat, Republican, Independent, or Other), and whether they voted in the last election (Yes, No). Each of the three students selects a random sample of 40 students and asks each student their political party and if they voted in the last election. Their three Mean Group Diff statistics are: Mean Group Diff 1 = 0.12 Mean Group Diff 2 = 0.35 Mean Group Diff 3 = 0.27 Which Mean Group Diff statistic provides the strongest evidence against the null hypothesis?

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Use the Goodness of Fit applet to conduct a theory-based chi-square goodness-of-fit test, and report the chi-square statistic and the p-value. chi-square statistic = p-value =

Hope student researchers want to determine if students yawning (when being yawned at) is asso-ciated with the time of day (morning, afternoon, and evening). They found the following results when they yawned in front of people around campus: • Morning: 25 of the 39 people yawned • Afternoon: 15 of the 38 people yawned • Evening: 29 of the 44 people yawned -The chi-square statistic for this test was 6.991. If instead, the chi-square statistic had been 5.332, would the p-value be smaller, larger, or remain the same?

Suppose we conduct a chi-square goodness-of-fit test to determine if a 6-sided die is fair. We roll the die 10 times, and the resulting p-value is very large. What may we conclude? Select all that apply.

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -For each BMI category, calculate the conditional proportion of people that browsed first and write these numbers below as decimals, not fractions. Bottom Third___________ Middle Third____________ Top Third____________

According to the 2019 U.S. Census Bureau estimates, 63.4% of the U.S. self-identifies as Non-Hispanic white, 15.3% as Hispanic and Latino, 13.4% as Black or African American, 5.9% as Asian, and 2.0% as Other. A random sample of 1000 students graduating from California colleges and universities resulted in the following data on self-identified race: You would like to determine if the distribution of self-identified race among California college and university students differs from the distribution of self-identified race in the U.S. overall. -Use the Goodness of Fit applet to conduct a simulation-based chi-square goodness-of-fit test using the chi-square statistic, and report the statistic and the p-value. Use at least 1000 shuffles. chi-square statistic = p-value =

Hope student researchers want to determine if students yawning (when being yawned at) is asso-ciated with the time of day (morning, afternoon, and evening). They found the following results when they yawned in front of people around campus: • Morning: 25 of the 39 people yawned • Afternoon: 15 of the 38 people yawned • Evening: 29 of the 44 people yawned -Follow-up confidence intervals for all pairwise differences in proportions are as follows: •0.0299 to 0.4627: Morning - Afternoon •-0.2237 to 0.1876: Morning - Evening •-0.4736 to -0.0551: Afternoon - Evening Based off of these intervals, which of the following conclusions are correct?

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -Fill in the following two-way table with the observed data.