Answer :
The t-test value for the given collected data of hours of studying and exam grade is equal to 10.45.
As given in the question,
n = 5
Mean of the data ( time ) μ₁ = ( 1+ 3 + 4 + 3+ 6)/ 5
= 3.4
Mean of the exam grade μ₂ = ( 55 + 75 + 80 + 85 + 99) / 5
= 78.8
Standard deviation of time σ₁ = 1.82
Standard deviation of exam grade σ₂ = 16.04
Standard error of time = σ₁/√n
= 1.82 / √5
=0.81
Standard error of time =σ₂/√n
= 16.04/ √5
=7.17
Difference in mean of time and exam grade = 78.8 - 3.4
= 75.4
Standard error of difference 'S.E'= √ (0.81)² + (7.17)²
= 7.215
t - test for the given data
= | μ₁ - μ₂| / S.E.
= | 3.4 - 78.8| / 7.215
= 75.4 / 7.215
= 10.45
P value and statistical significance:
Two-tailed P value is smaller than 0.0001
Therefore, the t-test value for the given collected data is equal to 10.45.
The above question is incomplete , the complete question is:
Researchers have collected data on the hours of studying in a week and the exam grade of a student. you are given the data below (10 points). hint: this questions is similar to q1 in hw7.
hours of studying exam grade
1 55
3 75
4 80
3 85
6 99
Calculate the t -test and interpret the data?
