Ch 11 Extra Credit Quiz

A toll collector wonders if drivers are equally likely to choose each of the three lanes at his toll booth. He selects a random sample of 465 drivers that approach the booth when all three lanes are empty, so that the driver’s choice isn’t influenced by the cars already at the booth. The table summarizes the data. Which of the following is an appropriate alternative hypothesis for addressing this question?

• The observed number of drivers choosing each lane is equal.

• The observed number of drivers choosing each lane is different from the expected numbers.

• The proportions of drivers choosing each of the three lanes are equal.

• Drivers are not equally likely to choose each of the three lanes.

• The proportions of drivers choosing each of the three lanes are all different.

A toll collector wonders if drivers are equally likely to choose each of the three lanes at his toll booth. He selects a random sample of 465 drivers that approach the booth when all three lanes are empty, so that the driver’s choice isn’t influenced by the cars already at the booth. The table summarizes the data. Which of the following is the correct expression for the chi-square statistic in this situation?

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Which of the following is a condition that must be met to carry out a chi-square test for goodness of fit?

• The population must be normally distributed, or the sample size must be greater than 30.

• The cell counts for the sample have to be approximately the same as the expected counts.

• All observed cell counts must be greater than 5.

• All expected counts must be greater than 5.

• More than one of these conditions must be met.

1. Mrs. Nataro wants to know if there is a difference in color preference between male and female toddlers? Researchers offer identical toys of four different colors to separate random samples of male and female children aged 12 to 18 months and record which color toy is picked up first. The results are given. Which of the following is the appropriate null hypothesis for this test?

• The distribution of first toy chosen is 25% for each color, regardless of gender.

• Males are more likely to choose a blue toy and females are more likely to choose a pink toy.

• The distribution of color is the same for male and female 12- to 18-month-old children.

• Color of first toy chosen is associated with gender in the population of 12- to 18-month old children.

• First toy chosen is independent of gender in the population of 12- to 18-month old children

Mrs. Nataro wants to know if there is a difference in color preference between male and female toddlers? Researchers offer identical toys of four different colors to separate random samples of male and female children aged 12 to 18 months and record which color toy is picked up first. The results are given. Under the assumption that the null hypothesis is true, which of the following represents the expected count for male children who chose a blue toy?

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Mrs. Nataro wants to know if there is a difference in color preference between male and female toddlers? Researchers offer identical toys of four different colors to separate random samples of male and female children aged 12 to 18 months and record which color toy is picked up first. The results are given. The chi-square statistic for these data is X2 = 8.134. Which of the following intervals contains the P-value for this test?

• 0.005 < P - value < 0.01

• 0.01 < P - value < 0.025

• 0.025 < P - value < 0.05

• 0.05 < P - value < 0.1

• P - value > 0.1

Children of three different ages (5 years, 7 years, and 9 years) were given a list of 5 different animals and asked which animal they would choose to be if they could be that animal for one day. Does the distribution of animal preference differ within these age groups? The conditions were verified and a chi-square test for homogeneity produced a P-value of 0.0847. Using a significance level of a = 0.05, which of the following is the appropriate conclusion?

• Reject H₀: there is convincing evidence that the distribution of animal choices is different for at least one of the age groups.

• Accept H₀: there is convincing evidence the distribution of animal choices is the same for all three age groups.

• Reject H₀: there is not convincing evidence that the distribution of animal choices is different for at least one of the age groups.

• Fail to reject H₀: there is convincing evidence the distribution of animal choices is the same for all three age groups.

• Fail to reject H₀: there is not convincing evidence that the distribution of animal choices is different for at least one of the age groups.

A consumer advocacy group surveys a random sample of car owners to determine if there are differences in the types of problems encountered with new cars made by different manufacturers. Each subject was asked to identify the brand of car they drove and the first problem they had that required repair. A partial Minitab output for a chi- square test is shown. Of the following, which test is appropriate in this setting?

• Chi-square test for homogeneity

• Chi-square test for independence

• Chi-square test for goodness of fit

• A chi-square test is not appropriate in this setting.

• Both Chi-square test for homogeneity and Chi-square test for independence are correct.

A consumer advocacy group surveys a random sample of car owners to determine if there are differences in the types of problems encountered with new cars made by different manufacturers. Each subject was asked to identify the brand of car they drove and the first problem they had that required repair. A partial Minitab output for a chi- square test is shown. For the appropriate chi-square test for these data, what are the correct degrees of freedom?

• 3

• 5

• 8

• 14

• 200

A consumer advocacy group surveys a random sample of car owners to determine if there are differences in the types of problems encountered with new cars made by different manufacturers. Each subject was asked to identify the brand of car they drove and the first problem they had that required repair. A partial Minitab output for a chi- square test is shown. Based on the original data and the contributions to the chi-square statistic for each cell in the two-way table, which of the following statements is true?

• The observed number of Hudsons requiring electrical work is much less than we would expect if the null hypothesis were true.

• The greatest difference between observed and expected counts is electrical repairs for Hudsons.

• The number of observed Hudsons requiring brake repair is much greater than we would expect if the null hypothesis were true.

• The cell that contributes the least amount to the chi-square statistic is Packards that need electrical work.

• The expected count of Hudsons requiring drive train repairs is the same as the expected count of Studebakers requiring drive train repairs.