Question

For each of the following studies, state both the null and alternative hypotheses and the decision rule, then work the problem. Look up the critical value of t that would cut off the tails of the distribution. Note that each study specifies the alpha value to use and whether to use a one- or two-tailed test. Decide whether to reject or fail to reject the null and answer the question.

The first example does not include a sample size, I just need the best answer that includes as much as is asked (null, alternative, decision rule and critical value)

1. Sommer (1999) investigated student satisfaction with distance learning. One group of students took Introductory Psychology over the Internet and another group took the course in the usual classroom lecture format. Students rated their satisfaction with the course on a scale from 1 (not at all satisfied) to 9 (extremely satisfied). Sommer found that students in the distance learning condition had an average satisfaction of 4.33, with a standard deviation of 2.94, whereas students in the classroom format reported a mean satisfaction of 6.67 and a standard deviation of 0.82. State your null hypothesis, use α = 0.05 for a nondirectional test, and report your critical value. Is there a difference between the groups?

2. Wilson (1999) studied impulse control in grade-school children. She studied 25 average third-graders and found a failure of impulse control 4.6 times per day, with a standard deviation of 2.1 times per day. Wilson also studied 36 third-graders diagnosed with ADHD and found that they showed failures of impulse control on average 7.2 times per day, with a standard deviation of 3.1. State your null hypothesis, use α = 0.01 for a directional test, and report your critical value. Do third-graders with ADHD have more trouble with impulse control?

Answer 1

(a) The Hypothesis:

The decision rule is that if tstat is - tcritical, or if tstat is t critical, then Reject H0.

Since s1/s2 = 2.94/0.82 is > 2, the degrees of freedom is given by the formula below

I have assumed sample sizes of 60 for long distance and 80 for classroom

The Test Statistic is given by

The critical values at = 0.05, df = 66 is -2 and +2

The Decision: Since t stat is < - critical, we reject H0.

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(b) (a) The Hypothesis:

The decision rule is that if tstat is - tcritical, .

Since s1/s2 = 2.1/3.1 is > 0.5 and <2, the degrees of freedom is given by the formula n1 + n2 - 2 = 25 + 36 - 2 = 59

The critical values at = 0.01, df = 59 is -2.39

We use pooled variance:

The Test Statistic is given by

The Decision: Since t stat is < - critical, we reject H0.

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