1. For each scenario, which statistical procedure is most appropriate (one sampl
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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. (16 points)
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 of World Campus advisors wants to know if there is a relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.
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
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)?
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.
Here we use one sample mean test.
The hypothesis for testing is,
H0 : mu = 100 Vs H1 : mu > 100
B. A team of World Campus advisors wants to know if there is a relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.
Here we use Chi-square test of indepedence.
Here we have to test the hypothesis that,
H0 : There is no relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.
H1 : There is a relationship in the population of all World Campus STAT200 students between using Penn State Learning’s free online tutoring services and passing STAT200.
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).
Here also we use chi-square test of independence.
The test of hypothesis is,
H0 : The vote response and their level of education are independent.
H1 : The vote response and their level of education are not independent.
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).
Here we use one sample proportion test.
Hypothesis for the test is,
H0 : p = p0 Vs H1 : p not= p0
where p is population proportion of preschool students like superheroes.
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).
Here we use chi-square test of independence.
The test of hypothesis is,
H0 : There is no linear relationship between between whether or not a child likes licorice and whether or not the child’s mother likes licorice.
H1 : There is a relationship between whether or not a child likes licorice and whether or not the child’s mother likes licorice.
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).
Here also we use chi-square test of independence.
The hypotheis for the test is,
H0 : There is no relationship between biological sex and whether or not an individual has sleep apnea.
H1 : There is a relationship between biological sex and whether or not an individual has sleep apnea.
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).
Here we use chi-square test of independence.
The hypothesis for the test is,
H0 : There is no relationship between gender (man/woman) and students’ intended major area.
H1 : There is a relationship between gender (man/woman) and students’ intended major area.
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. 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.
Here we use one way ANOVA :
The hypothesis for the test is,
H0 : mu1 = mu2 = mu3 Vs H1 : Atleast one of the mean is differ than 0.
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