AP Statistics Unit Review

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 or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at the current levels. The results are given in the table. The conditions for carrying out the chi-square test is: I. Separate random samples from the populations of interest II. Expected counts large enough III. The samples themselves and the individual observations in each sample are independent. Which of the conditions is (are) satisfied in this case?

• I only

• II only

• I and II only

• II and III only

• I, II and III

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. We wish to test H0: The racial distribution of traffic tickets in the city is the same as the racial distribution of the city’s population. We compute the value of X2 to be 6.58. Assuming the conditions for inference are met, the p-value of our test is

• greater than 0.2

• between 0.10 and 0.20

• between 0.05 and 0.10

• between 0.01 and 0.05

• less than 0.01

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. We wish to test H0: The racial distribution of traffic tickets in the city is the same as the racial distribution of the city’s population. The category that contributes the largest component to the X2 statistic is

• White

• Black

• Hispanic

• Other

• The answer cannot be determined since this is only a sample

All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate this, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Data is given in the table. Computer software was used to analyze the data. X² = 0.082 + 0.170 + 0.023 + 0.048 + 0.099 + 0.013 = 0.435. A Type I error would occur if we conclude that

• HCC wiring caused cancer when it actually didn’t. 
  

• HCC wiring didn’t cause cancer when it actually did. 
  

• There is no association between the type of wiring and the form of cancer when there actually is an association.
  

• There is an association between the type of wiring and the form of cancer when there actually is no association.
  

• The type of wiring and the form of cancer have a positive correlation when they actually don’t. 
  

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 and 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?" The table shows the data. 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 = .25, where p = the proportion of all students that prefer Asian food.

• H₀ : n_A = n_M = n_P = n_H = 25, where n_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 = .25, where p_A is the proportion of students in the school who would choose Asian food, and so on.

• H₀ : p̂_A = p̂_M = p̂_P = p̂_H = .25, where p̂_A is the number of students in the sample who would choose Asian food, and so on.

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 and 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?" The table shows the data. The chi-square statistic is

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 and 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?" The table shows the data. The P-value for a chi-square test for goodness of fit is 0.0129.  Which of the following is the most appropriate conclusion?

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

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

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

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

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

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

• 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 was "What do you think are the chances you will be married in the next ten years?" Above is a two-way table of the responses by gender. The degrees of freedom for the chi-square test for this two-way table are:

• 4

• 8

• 10

• 20

• 4876

A Chi-square goodness-of-fit test is used to test whether a 0 - 9 spinner is “fair” (that is, the outcomes are all equally likely). The spinner is spun 100 times and the results are recorded. The degrees of freedom for the test will be

• 8

• 9

• 10

• 99

• none of these