1. For each scenario, which statistical procedure is most appropriate (one sampl
ID: 3154747 • Letter: 1
Question
1. For each scenario, which statistical procedure is most appropriate (one sample mean, one sample proportion, two independent proportions, two independent means, two paired/dependent means, one-way ANOVA, chi-square test of independence)? EXPLAIN WHY.
A. The honors college at one large university wants to know if their accepted students have an average IQ that is higher than the known national average of 100.
B. A team advisors want to know if there is a relationship in the population of all students between using the Learning’s free online tutoring services and passing class.
C. A group of political science students wants to know if there is a relationship between whether someone is registered to vote or not and their level of education. They take a sample of 200 people and ask if they are registered to vote (yes or no) and ask for their level of education (no college degree, college degree).
D. A preschool teacher wants to know if four-year-old boys and girls differ in terms of whether or not they like superheroes. He takes a representative sample of 30 preschool students, records each child’s gender, and asks if they like superheroes (yes/no).
E. Food scientists want to know if there is a relationship between whether or not a child likes licorice and whether or not the child’s mother likes licorice. They take a sample of 50 child-mother pairs and ask each individual if they like licorice (yes/no).
F. A team of sleep scientists wants to know if there is a relationship between biological sex and whether or not an individual has sleep apnea. They take a sample of 500 individuals and record their biological sex (male/female) and if they have sleep apnea (yes/no).
G. An admissions counselor at a technical college wants to know if there is a relationship between gender (man/woman) and students’ intended major area (computer science, automotive mechanics, culinary arts, cosmetology).
H. A group of psychology students wants to compare the anxiety levels of test takers who are given a dog, cat, or teddy bear to pet. They take a sample of 120 introductory psychology students. Participants are randomly assigned to one of the three treatment conditions (dog, cat, teddy bear). After the testing sessions the experimenters administer an anxiety survey to each participant. Scores on the anxiety scale are quantitative.
Explanation / Answer
A. The sample mean(xbar) is average IQ of the accepted students and the population mean(µ) is provided by the national average as equal to 100. We simply need to conduct a test to find if the sample mean is higher than the national/population mean. Hence we conduct a one sample mean test.
B. The population of all the students is tested to know a relation between online classes taken and passing the class. In this case after the data is collected it can be divided into two groups: group I -taking online classes and group II: Not taking online classes
There after average number of students passing in each group can be compared with the help of the test "Compare two independent means" test
C. In this case a sample of 200 students is considered and they are categorised under registration and education level heads. We need to test if there exist any relationship between these two factors. The two variables here are both categorical. The best test to check their independence is the Chi sqaure test.
D. We need to compare four year old boys and girl in terms of liking superheros. Again as the data is colelcted for 30 kids, there gender and liking for superheroes is recorded. Thereafter the data is divided into two groups: Boys and girls. In each group we can obtain the proportion of those who like superheroes. Since we are comparing the proportions of the two groups the best test is "Compare two independent proportions"
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