1) For each of the following studies, say whether you ...



1) For each of the following studies, say whether you would use a t test for dependent means or a t test for independent means.

a) A researcher randomly assigns a group of 25 unemployed workers to receive a new job skills program and 24 other workers to received the standard job skills program, and then measures how well they all do on a job-skills test.

“randomly assigns” and n=25 (so can’t have equal numbers in two groups) are both keys that help us know that we must use an independent samples t-test

b) A researcher measures self-esteem in 21 students before and after taking a difficult exam

“before and after” is a key phrase that helps us know that we must use an related (dependent) samples t-test(this is a repeated measures design)

c) A researcher tests reaction time of each of a group of 14 individuals twice, once while in a very hot room and once while in a normal-temperature room.

“tests reaction time of a group … twice” is a key phrase that helps us know that we must use an related (dependent) samples t-test (this is a repeated measures design)

2) A developmental psychologist compares 4-year olds and 8-year olds on their ability to understand the analogies used in stories. The scores for the five 4-yr olds were 7, 6, 2, 3, and 8. The scores for the three 8-yr olds were 9, 2, and 5. Using an alpha level of 0.05, do older children do better?

a) Use the 5 steps of hypothesis testing

H0: The analogy scores for 4-year olds and 8-year olds are not different (or even that the scores for 8 year olds are lower): (m4yr− - m8yr −) < 0 mins

HA: The analogy scores for 8-year olds are higher than those for 4-year olds: (m4yr− - m8yr −) > 0

She predicted better scores for the 8-year olds, so this means that we should use a 1-tailed test. Also the problem states that a = 0.05. So that makes our tcrit (with df = n4yr + n8yr – 2 = 5) = -2.02 (negative because we’re looking subtracting 8-year olds scores from 4-year olds scores, so we look in the lower tail)

We need to compute the mean and standard deviation for the sample.

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Now we need to compute the estimated standard error (and along the way pooled variance)

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Now we need to compute the t-test (one sample t-test)

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Now we compare this tobs with the tcrit

-0.36 is not in the critical region (which is scores -2.02 and lower), so we fail to reject the null hypothesis and conclude that there is no support that the 8-year olds have higher analogy scores.

b) sketch the distributions involved

c) explain your conclusions

While there is a numerical increase in analogy understanding for the 8-year olds, this numerical increase is not above and beyond what one might expect based on random sampling error (it is not a statistically significant difference).

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