AP Statistics Chapter 11

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year.  She wants to know if each type of food will be equally popular so she can start ordering supplies.  To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?"  Here are the data in the table provided.  Identify the p-value and decide which of the following is the most appropriate conclusion?

• Because 0.0129 is less than α = 0.05, fail to reject H₀.  There is convincing evidence that the food choices are equally popular.

• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are not equally popular.

• Because 0.0289 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are not equally popular.

• Because 0.0289 is less than α = 0.05, fail to reject H₀.  There is not convincing evidence that the food choices are equally popular.

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education.  To offset the reduction, the largest state university proposed a 25% tuition increase.  It was determined that such an increase was needed simply to compensate for the lost support from the state.  Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels.  The results are in the table provided.  Why hypotheses would be appropriate for performing a chi-square test?

• The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases.  The alternative is that how close students are to graduation makes no difference in their opinion.

• The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years.  The alternative is that the mean is different for at least 2 of the 4 years.

• The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university.  The alternative is that the distribution is different for at least 2 of the 4 years.

• The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent.  The alternative is that these variables are dependent.

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  Assuming H₀ is true, the expected number of Hispanic drivers who would receive a ticket is

• 10.36

• 11

• 11.84

• 12

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  We compute the value of the χ² statistic to be 6.58.  Assuming that the conditions for inference are met, the P-value of our test is

• Between 0.10 and 0.20.

• Between 0.05 and 0.10.

• Between 0.01 and 0.05.

• Less than 0.01.

• A

• B

• C

• D

• E

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Is this a probability distribution?

• No

• Yes

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  The category that contributes the largest component to the χ² statistic is

• White.

• Black.

• Hispanic.

• Other.

All current-carrying wires produce electro-magnetic (EM) radiation.  High-frequency EM radiation is thought to be a cause of cancer.  The lower frequencies are generally assumed to be harmless.  To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either high-current configuration (HCC) or low-current configuration (LCC).  The data is provided in a table.  Which of the following may we conclude, based on the test results?

• There is convincing evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.

• HCC either causes cancer directly or is a major contributing factor to the development of cancer in children.

• There is not convincing evidence of an association between wiring configuration and the type of cancer that cause the deaths of children in the study.

• There is convincing evidence that HCC does not cause cancer in children.

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

• H₀: μ = 25, where μ = the mean number of students that prefer each type of food.

• H₀: p = 0.25, where p = the proportion of all students who prefer Asian food.

• H₀: η_A = η_M = η_P = η_H = 0.25, where η_A is the number of students in the school who would choose Asian food, and so on.

• H₀: p_A = p_M = p_P = p_H = 0.25, where η_A is the proportion of students in the sample who would choose Asian food, and so on.