AP Statistics Unit 6 Review

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• B

• C

• D

• E

• A

• B

• C

• D

Suppose you take a random sample of 25 from a population with a mean of 120 and a standard deviation of 15. Your sample has a mean of 115 and a standard deviation of 13.8. Which of the following has a mean of 120 and a standard deviation of 3?

• The distribution of the population

• The distribution of the sample data

• The sampling distribution of the sample mean

• The sampling distribution of the population mean

• No important distribution related to this situation has the given mean and sd.

500 random samples of size n= 900 were taken from a large population in which 10% of the subjects are left handed. The proportion of the subjects in that sample that is left handed is found for each sample and a histogram of these 500 proportions is drawn. Which interval covers the range in which about 68% of the values in the histogram will fall.

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. For these data, χ2 = 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 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 and type II error because the calculations are correct

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. Which 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 opinions.

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

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

• The null hypothesis is that there is an association between year in school and opinion about the tuition increase at this university. The alternative hypothesis is that these variables are not associated.

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. Assuming H0 is true, the expected number of Hispanic drivers who would receive a ticket is

• 8

• 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. 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

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 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.