Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks, such as problem solving (Linde & Begrstroem, 1992). To demonstrate this phenomenon, one sample of n=25 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second scores was recorded. For this sample, the students averaged MD=4.7 points better on the first test with a variance of s^2=64 for the different scores. 1. State the hypotheses both experimental and statistical. 2. Do the data indicate a significant decline in problem-solving ability? Use a one-tailed test with a=.01. Please show work and state your decision regarding the H0. 3. Compute a 90% Confidence Interval (upper and lower values). 4. State your conclusion in APA format

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks, such as problem solving (Linde & Begrstroem, 1992). To demonstrate this phenomenon, one sample of n=25 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second scores was recorded. For this sample, the students averaged MD=4.7 points better on the first test with a variance of s^2=64 for the different scores.

1. State the hypotheses both experimental and statistical.

2. Do the data indicate a significant decline in problem-solving ability? Use a one-tailed test with a=.01. Please show work and state your decision regarding the H0.

3. Compute a 90% Confidence Interval (upper and lower values).

4. State your conclusion in APA format.

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