STAT CH 11
In which of the following situations should the chi-square Test for Independence be used? A company wants to determine if its employees have sick days that are uniformly distributed across the days of the week. They collect data on the number of sick days taken on different days of the week and compare the distribution to the uniform distribution. A company is trying to determine whether employees are overworked. They ask employees whether they feel overworked or not. As part of the survey, they also record the work department of each employee. The data are summarized in a contingency table. They want to determine if being overworked depends on the department of an employee. A professor wants to determine if the men and women in her class had the same distribution of grades. She records the grade distribution for each gender and compares the two distributions.
A company is trying to determine whether employees are overworked. They ask employees whether they feel overworked or not. As part of the survey, they also record the work department of each employee. The data are summarized in a contingency table. They want to determine if being overworked depends on the department of an employee. The Test of Independence determines if two variables (or factors) are independent or dependent. In this case, that applies to the company that is trying to decide if being overworked is dependent on work department.
In which of the following situations should the chi-square Test for Independence be used? A researcher is trying to determine if salaries for male and female teachers have the same distribution. She surveys a random sample of teachers and records the distribution of salaries for each gender. He wants to determine if the distributions are the same. A professor wants to determine if the students in each of her two sections had the same distribution of grades. She records the grade distribution for each section and compares the two distributions. A market research company puts out a survey asking people two questions. First, it asks which brand of detergent they use. Second, it asks whether the household has more than one car or not. The data are collected and recorded in a contingency table. The company wants to determine if there is a relationship between the brand of detergent and car ownership.
A market research company puts out a survey asking people two questions. First, it asks which brand of detergent they use. Second, it asks whether the household has more than one car or not. The data are collected and recorded in a contingency table. The company wants to determine if there is a relationship between the brand of detergent and car ownership. The Test of Independence determines if two variables (or factors) are independent or dependent. In this case, that applies to the company that is trying to decide if detergent brand is dependent on car ownership.
In which of the following situations should the chi-square Test for Goodness-of-Fit be used? A survey company puts out a survey asking people two questions. First, it asks if a person uses public transportation or not. Second, it asks whether or not the person supports an upcoming environmental protection bill. The data are recorded in a contingency table. The company wants to determine if support for the bill is independent of public transportation usage. A researcher is trying to determine if boys and girls spend a similar amount of time on homework. He surveys a random sample of boys and girls in a school and records the distribution of time spent on homework for each gender. He wants to determine if the distributions are the same. A referee wants to make sure the coin he uses for the opening coin toss is fair. He flips the coin 30 times and compares the number of heads and tails with the numbers he would expect to get if the coin were fair.
A referee wants to make sure the coin he uses for the opening coin toss is fair. He flips the coin 30 times and compares the number of heads and tails with the numbers he would expect to get if the coin were fair. The Goodness-of-Fit Test determines if data fit a particular distribution. It is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution.In this case, that applies to the referee comparing the number of heads and tails with the expected number of heads and tails.
In which of the following situations should the chi-square Test for Homogeneity be used? A casino wants to decide if a certain pair of dice is fair. They roll the dice 100 times and compare the distribution of outcomes with the expected distribution of outcomes if the dice were fair. A market research company puts out a survey asking people two questions. First, it asks which brand of detergent they use. Second, it asks whether the household has more than one car or not. The data are collected and recorded in a contingency table. The company wants to determine if there is a relationship between the brand of detergent and car ownership. A researcher is trying to determine if salaries for male and female teachers have the same distribution. She surveys a random sample of teachers and records the distribution of salaries for each gender. She wants to determine if the distributions are the same.
A researcher is trying to determine if salaries for male and female teachers have the same distribution. She surveys a random sample of teachers and records the distribution of salaries for each gender. She wants to determine if the distributions are the same. The Test for Homogeneity is used to determine if two populations with unknown distributions have the same distribution as each other. In this case, that applies to the researcher trying to determine if salaries for male and female teachers have the same distribution.
A professor expects that the grades on a recent exam are normally distributed with a mean of 80 and a standard deviation of 10. She records the actual distribution of grades and wants to compare it to the normal distribution.Which of the following χ2 tests should be used in the situation above? Test of Independence Goodness-of-Fit Test Test for Homogeneity
Goodness-of-Fit Test The Goodness-of-Fit Test determines if data fit a particular distribution. It is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution.In this case, the professor wants to compare the distribution of scores with the normal distribution, so the Goodness-of-Fit Test is most appropriate.
A casino claims that a certain game has 13 probability of winning a dollar, 13 probability of losing a dollar, and 13 probability of breaking even. Some statistics students want to test that claim, so they play the game 60 times, and compare the number of different outcomes to the distribution that the casino claimed.Which of the following χ2 tests should be used in the situation above? Test of Independence Goodness-of-Fit Test Test for Homogeneity
Goodness-of-Fit Test The Goodness-of-Fit Test determines if data fit a particular distribution. It is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution.In this case, the statistics students are comparing the actual outcomes in the casino game with the distribution that the casino claimed, so the Goodness-of-Fit Test is the most appropriate.
A professor is trying to determine if her students guessed on a certain multiple choice question. She expects that if the students guessed, the distribution of answers would be uniform for that question. She compares the observed distribution of answers with the uniform distribution. The professor conducts a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) Select the correct null and alternative hypotheses for this test. H0: The student answers have the uniform distribution. H0: The student answers do not have the uniform distribution. Ha: The student answers do not have the uniform distribution. Ha: The student answers have the uniform distribution.
H0: The student answers have the uniform distribution. Ha: The student answers do not have the uniform distribution. For the chi-square Goodness-of-Fit test, the null hypothesis assumes the expected distribution and looks at how likely the observed data is under that assumption. So the hypotheses will always look like: H0: The variable has the specified distribution. Ha: The variable does not have the specified distribution.
Key Terms Chi-square distribution: used to describe data and statistics that are positive and right skewed. The chi-square distribution has one parameter, degrees of freedom (df). Goodness-of-fit test: a hypothesis test that determines if data, classified into several groups, resemble a particular distribution Chi-square test of independence: a hypothesis test that determines if two variables (or factors) are independent Chi-square test of homogeneity: a hypothesis test that determines if two populations have the same distribution
Key Terms Chi-square distribution: used to describe data and statistics that are positive and right skewed. The chi-square distribution has one parameter, degrees of freedom (df). Goodness-of-fit test: a hypothesis test that determines if data, classified into several groups, resemble a particular distribution Chi-square test of independence: a hypothesis test that determines if two variables (or factors) are independent Chi-square test of homogeneity: a hypothesis test that determines if two populations have the same distribution
A university admissions officer is trying to determine if men and women have similar acceptance rates across the different schools at the university (engineering, arts and sciences, business). She finds the distribution of acceptances for each gender across the three schools and wants to compare the distributions.Which of the following χ2 tests should be used in the situation above? Test of Independence Goodness-of-Fit Test Test for Homogeneity
Test for Homogeneity The Test for Homogeneity is used to determine if two populations with unknown distributions have the same distribution as each other.In this case, the college is trying to determine if acceptances of men and women have the same distribution across the three schools, so the Test for Homogeneity is appropriate.
A hospital is trying to compare the weights of babies born at night and babies born during the day. They collect a random sample of weights for babies born at night and during the day and record the distribution of each. They want to compare the distributions to see if they are the same.Which of the following χ2 tests should be used in the situation above? Test of Independence Goodness-of-Fit Test Test for Homogeneity
Test for Homogeneity The Test for Homogeneity is used to determine if two populations with unknown distributions have the same distribution as each other.In this case, the hospital is trying to determine if the distributions for babies born during the day and during the night are the same, so the Test for Homogeneity is appropriate.
A survey company puts out a survey asking people two questions. First, it asks if a person owns a car or not. Second, it asks whether or not the person supports an upcoming environmental protection bill. The data are recorded in a contingency table. The company wants to determine if support for the bill depends on car ownership.Which of the following χ2 tests should be used in the situation above? Test of Independence Goodness-of-Fit Test Test for Homogeneity
Test of Independence The Test of Independence determines if two variables (or factors) are independent or dependent. Because the company is trying to determine if there is a relationship between car ownership and support for the environmental bill, the Test of Independence is the most appropriate test.
Which of the following is a characteristic of the chi-square distribution? Select all correct answers. The chi-square curve is skewed to the right. The chi-square curve is symmetrical. The chi-square curve is nonsymmetrical. The total area under the χ2-curve is equal to the degrees of freedom, df.
The chi-square curve is skewed to the right. The chi-square curve is nonsymmetrical. The following are all characteristics of the chi-square distribution. The chi-square curve is skewed to the right (it has a long tail to the right). The chi-square curve is nonsymmetrical, because it is skew to the right. The mean of the chi-square distribution is located to the right of the peak, because being skew to the right pulls the mean to the right. The total area under the χ2-curve is equal to 1, as is the case for any probability density function As the degrees of freedom increases, the chi-square curves look more and more like a normal curve. The chi-square curve approaches, but never touches, the positive horizontal axis, because the long right tail is technically never 0.
