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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A cognitive psychologist is interested in whether increasing reading speed improves comprehension. He has students complete a reading
comprehension task before and after a six-week speed-reading course.
In the beginning of the study, a randomly selected group of 81 students scored an average of 102 points on the reading comprehension task. Since
the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of Mp is normal. He plans to use a repeated-
measures t test.
The cognitive psychologist identifies the null and alternative hypotheses as:
Hi : PD
Use the Distributions tool to find the critical region(s) for a = 0.05.
The critical t score, which is the value for t scores that separates the tail(s) from the main body of the distribution and forms the critical region(s), is
(Hint: Remember to set the degrees
freedom on the tool and to consider whether this is a one-tailed or two-tailed test.)
t Distribution
Degrees of Freeoom - 06
s000
3.0
-2.0
20
3.0
-1.0
0.0
1.0
4.0
-0.677 0.00o 0.677
Transcribed Image Text:A cognitive psychologist is interested in whether increasing reading speed improves comprehension. He has students complete a reading comprehension task before and after a six-week speed-reading course. In the beginning of the study, a randomly selected group of 81 students scored an average of 102 points on the reading comprehension task. Since the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of Mp is normal. He plans to use a repeated- measures t test. The cognitive psychologist identifies the null and alternative hypotheses as: Hi : PD Use the Distributions tool to find the critical region(s) for a = 0.05. The critical t score, which is the value for t scores that separates the tail(s) from the main body of the distribution and forms the critical region(s), is (Hint: Remember to set the degrees freedom on the tool and to consider whether this is a one-tailed or two-tailed test.) t Distribution Degrees of Freeoom - 06 s000 3.0 -2.0 20 3.0 -1.0 0.0 1.0 4.0 -0.677 0.00o 0.677
The critical t score, which is the value for t scores that separates the tail(s) from the main body of the distribution and forms the critical region(s), is
(Hint: Remember to set the degrees of freedom on the tool and to consider whether this is a one-tailed or two-tailed test.)
t Distribution
Degrees of Freegom- 05
So00
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
-0.677 0.000 0.677
After the speed-reading course, the students scored an average of 4 points higher than before they began the speed-reading course. The standard
deviation of the difference scores was s = 22.
To calculate the t statistic, you must first calculate the estimated standard error. The estimated standard error is
(Note: For best
results, retain at least four decimal places from your calculation of the estimated standard error for use in calculating the t statistic.)
Calculate thet statistic. The t statistic is
Use the tool to evaluate the null hypothesis. Thet statistic
▼ in the critical region for a one-tailed hypothesis test. Therefore, the null
hypothesis is
. The cognitive psychologist
conclude that increasing reading speed improves comprehension.
Transcribed Image Text:The critical t score, which is the value for t scores that separates the tail(s) from the main body of the distribution and forms the critical region(s), is (Hint: Remember to set the degrees of freedom on the tool and to consider whether this is a one-tailed or two-tailed test.) t Distribution Degrees of Freegom- 05 So00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -0.677 0.000 0.677 After the speed-reading course, the students scored an average of 4 points higher than before they began the speed-reading course. The standard deviation of the difference scores was s = 22. To calculate the t statistic, you must first calculate the estimated standard error. The estimated standard error is (Note: For best results, retain at least four decimal places from your calculation of the estimated standard error for use in calculating the t statistic.) Calculate thet statistic. The t statistic is Use the tool to evaluate the null hypothesis. Thet statistic ▼ in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is . The cognitive psychologist conclude that increasing reading speed improves comprehension.
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