When I Was a Student at the University of Michigan

Question

Examlex · Accepted Answer

The Answer is a. Independent samples t test.
b. 1-tailed, because the researcher clearly expects Michigan students to score higher than BU students, on average.
c. Michigan mean > BU mean.
d. If I make Michigan the X1 variable and BU the X2 variable, I would expect a positive t value (because I expect Michigan students to have the higher mean). If the Xs are reversed, I would expect a negative t value. Using an alpha level of .05, 1-tailed, and 120 df (61 + 61 -2 = 120), my critical t value would be 1.658.
e. First I need to calculate standard errors of the mean for each sample.
For Michigan,

S_{\bar{x}}

= 200/7.81 =25.61. For BU students,

S_{\bar{x}}

= 150/7.81 = 19.21.
Then I square each

S_{\bar{x}}

: (25.61)² = 655.87. (19.21)² = 369.02. When I add these together I get 1024.89. Take the square root of that and I get 32.01. So my observed t = 600 - 565 / 32.01

\rightarrow

35 / 32.01 = 1.09. So my observed t value of 1.09 is less than the critical t value of 1.658. Therefore, I conclude that, in the population of Michigan students and BU students, the average SAT scores are equal. The difference in sample means is too likely due to chance for me to conclude that it was not.
f. Maybe Michigan undergrads really aren't any better than BU undergrads. Ugh.

When I Was a Student at the University of Michigan

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