STAT 218 Quiz 2

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Economics

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Feb 20, 2024

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Jordan Wattles Total score: 14 Quiz 2 Do Greek students have a higher GPA than non-Greek students? Sample of 45 Greeks showed their average GPA was 2.89 with a standard deviation of .32 while a sample of 32 non-Greek students showed an average GPA of 2.99 with a standard deviation of .27. a) What type of statistical procedure should we be using here? (1 pt) Observational study b) Is it appropriate to use normal approximation here? (1) no c) Write the null and alternative hypothesis in words and in symbols (4 pts) null: the LRA of GPAs of Greek students is the same as the GPAs of non-Greek students alternative: the LRA of GPAs of Greek students is less than the GPAs of non-Greek students H o : u g -u n = 0
H a : u g -u n < 0 d) Calculate the standardized statistics. (4) 2.89 − 2.99 . 32 2 45 + . 27 2 32 = − .1 .1024 45 + .0729 32 = − .1 2 √ .0023 + .0023 = − .1 .0678 = -1.475 e) Calculate AND interpret a 95% confidence interval to test the hypotheses above (2 pts) stat ± critical x error (2.89-2.99) ± 2 x .0678 -.1 ± .1356 (-.2356. .0356) f) Write a conclusion based on the confidence interval. (2 pts) Fail to reject the null because the interval includes the value 0, therefore not providing enough evidence to reject that u g -u n < 0.
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