Question

 

(1) What statistical test is appropriate?

The tests to choose from are:

• One-sample t-test
• Independent t-test (unpaired t-test)
• Paired t-test
• F-test
• ANOVA
• Correlation
• Regression
• Chi-square test for association between factors (independent Chi-square)
• Chi-square goodness of fit

(2) Why (explain your justification for using that test)?

(3) As appropriate for the data and the test, label your dependent variables, independent variables and factors (if present). (This one only applies to some kinds of tests!)

Scenario 1: A professor always gives his students two midterm exams, each out of 100 points. He wants to know if student performance on exams improves over the course of the semester.

Scenario 2: Another professor also gives two midterm exams over the semester. She wants to know if student performance on the final exam can be predicted from performance on the two midterm exams.

Scenario 3: An ice cream shop wants to compare men and women in terms of preference for eating their ice cream out of a cone or a bowl to determine if there is a gender difference. They take a sample of 500 customers (240 men and 260 women) and ask if they prefer cones over bowls. They found that 124 men preferred cones and 90 women preferred cones. Is there a gender difference in cone preference?

Scenario 4: Three professors were each teaching one section of a course. They all gave the same final exam and they want to know if there are statistical differences between how their students do on the exam.

Answer 1

Scenario 1: A professor always gives his students two midterm exams, each out of 100 points. He wants to know if student performance on exams improves over the course of the semester.

Independent t-test (unpaired t-test)

here we want to test difference of marks of  two sample of students and in each sample obtaining marks is independent to each other.

Scenario 2: Another professor also gives two midterm exams over the semester. She wants to know if student performance on the final exam can be predicted from performance on the two midterm exams.

Regression

regression analysis is a set of statistical processes for estimating the relationships among variables. here we want to make the relationship between final , midterm1 and midterm2

Scenario 3: An ice cream shop wants to compare men and women in terms of preference for eating their ice cream out of a cone or a bowl to determine if there is a gender difference. They take a sample of 500 customers (240 men and 260 women) and ask if they prefer cones over bowls. They found that 124 men preferred cones and 90 women preferred cones. Is there a gender difference in cone preference?

Chi-square test for association between factors (independent Chi-square)

the chi-square=sum((O-E)2/E)=23.94 with (r-1)(c-1)=(2-1)(2-1)=1 df

the critical chi-square(0.05,1)=3.84 is less than calculated chi-square=23.94, so we conclude there is association between gender and cone preferences ( there is a gender difference in cone preference)

	Observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	124	214*240/500	102.72	21.28	4.41
	90	286*240/500	137.28	-47.28	16.28
	116	214*260/500	111.28	4.72	0.20
	170	286*260/500	148.72	21.28	3.04
sum	500		500	0	23.94

Scenario 4: Three professors were each teaching one section of a course. They all gave the same final exam and they want to know if there are statistical differences between how their students do on the exam.

ANOVA

if we want to test difference among the two or more sample mean , we go for one-way anova