AP Statistics Unit 8 MC Questions

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To nd out, she selects a random sample of 100 students and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Below is her data. An appropriate null hypothesis to test whether the food choices are equally popular is

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Mrs. Nataro wants to know if male and female toddlers have different color preferences? 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. Here are the results: Which of the following is the appropriate null hypothesis for this test?

• The distribution of color preference 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 preference is the same for male and female 12- to 18-month-old children.
• Color preference is associated with gender in the population of 12- to 18-month-old children.
• Color preference is independent of gender in the population of 12- to 18-month-old children.

Mrs. Nataro wants to know if male and female toddlers have different color preferences? 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. Here are the results: 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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The chi-square statistic for these data is chi-squared=8.134. Which of the following 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

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked, “What do you think are the chances you will be married in the next 10 years?” Below is a two-way table of the responses by gender. Which of the following is the appropriate null hypothesis for performing a chi-square test?

• Equal proportions of female and male teenagers are almost certain they will be married in 10 years
• There is no difference between the distributions of female and male teenagers’ opinions about marriage in this sample.
• There is no difference between the distributions of female and male teenagers’ opinions about marriage in the population.
• There is no association between gender and opinion about marriage in the sample.
• There is no association between gender and opinion about marriage in the population.

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 below summarizes the data: Which of the following is an appropriate alternative hypotheses 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 below summarizes the data: Which of the following is the correct expression for the chi-square statistic in this situation?

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The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked, “What do you think are the chances you will be married in the next 10 years?” Below is a two-way table of the responses by gender. Which of the following is the expected count of females who respond "Almost certain"?

• 487.7
• 525
• 965
• 1038.8
• 1174

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked, “What do you think are the chances you will be married in the next 10 years?” Below is a two-way table of the responses by gender. Which of the following is the correct number of degrees of freedom for the chi-square test using these data?

• 4
• 8
• 10
• 20
• 4876

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked, “What do you think are the chances you will be married in the next 10 years?” Below is a two-way table of the responses by gender. For these data, chi-square = 69.8 with a P-value of approximately 0. Assuming that the researchers used a significance level of 0.05, which of the following is true?

• A Type I error is possible.
• A Type II error is possible.
• Both a Type I and a Type II error are possible.
• There is no chance of making a Type I or Type II error because the P- value is approximately 0.
• There is no chance of making a Type I or Type II error because the calculations are correct.