Q1) Independent-Samples t Test (20 points total) A high school teacher would lik

Question

Q1) Independent-Samples t Test (20 points total) A high school teacher would like to know whether students who have participated in a test prep program score significantly higher on a standardized test than those who have not participated in such a program. She collects the percentile scores from a test prep group of 10 students and a control group (no test prep) of 10 students. Both groups contain only female students and all students have similar school grades. The teacher thinks that the test prep group should out-perform the control group on the standardized test but would like to leave the hypothesis non-directional and run a two-tailed test, which is more stringent. She sets the significance level at : .05. For the questions below, the prep group is designated as sample 1 (drawn from population 1) and the control group is designated as sample 2 (drawn from population 2) Prep group IDTest score P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Control group IDTest score C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 84 80 87 90 76 73 82 80 72 80 82 86 81 83 80 68 80 82

Explanation / Answer

g)
variance of sample 1 = 14.8889
variance of sample 2 = 22.2222

h)
std. dev of sample 1 = 3.8586
std. dev of sample 2 = 4.7140

i)
pooled variance = 18.56
SE = sqrt(18.56*(1/7+1/7)) = 2.3028
Test statistic,
t = (83 - 77)/2.3028
t = 2.6055

j)
df = 10 + 10 - 2 = 18
critical value of t = -2.1009, 2.1009

k)
As calculated value of t lies beyond the critical value, we reject the null hypothesis.

m)
pooled std. dev. = sqrt(18.56) = 4.3081

m)
Based on above test we can conclude that test prep program worked.

  

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