Twenty students randomly assigned to an experimental group receive an instructio
ID: 2956359 • Letter: T
Question
Twenty students randomly assigned to an experimental group receive an
instructional program; 30 in a control group do not. After 6 months, both groups
are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, what should the experimenter conclude? (a) Use the steps of hypothesis testing, (b) sketch the distributions involved, and (c) explain your
answer to someone who is familiar with the t test for a single sample but not
with the t test for independent means.
Explanation / Answer
Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.x-bar = 25 ; s = 1.1952
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Using the .05 level of significance, what should we conclude about the
theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?)
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(a) Use the steps of hypothesis testing.
Ho: u = 24
Ha: u is not equal to 24
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t(25) = (25-24)/[1.1952/sqrt(8)] = 2.3665
p-value = 2P(t> 2.3665 with df=7) = 2*0.0249 = 0.0499
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Conclusion: At the 5% significance level, reject Ho
because the p-value is less than 5%.
Note: They don't get any closer than this.
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(b) Sketch the distributions involved.
Have to leave that to you.
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(c) Given the significance level, we find the critical value which defines the minimum difference between the mean and hypothesized value to make it statistically significant. We find our t-score is just greater than critical t, so this small difference is statistically significant, making natural cycle different from 24 hours. Given the significance level, we find the critical value which defines the minimum difference between the mean and hypothesized value to make it statistically significant. We find our t-score is just greater than critical t, so this small difference is statistically significant, making natural cycle different from 24 hours. Given the significance level, we find the critical value which defines the minimum difference between the mean and hypothesized value to make it statistically significant. We find our t-score is just greater than critical t, so this small difference is statistically significant, making natural cycle different from 24 hours. Given the significance level, we find the critical value which defines the minimum difference between the mean and hypothesized value to make it statistically significant. We find our t-score is just greater than critical t, so this small difference is statistically significant, making natural cycle different from 24 hours.
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