A cognitive psychologist is interested in whether taking a speed-reading course increases reading speed. She has students complete a reading speed test before and after a six-week speed-reading course. In the beginning of the study, a randomly selected group of 121 students scored an average of 252 words per minute on the reading speed test. Since the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of M D D is normal. She plans to use a repeated-measures t test. The cognitive psychologist identifies the null and alternative hypotheses as: H₀ : μ D D 0 H₁ : μ D D 0 Use the Distributions tool to find the critical region(s) for α = 0.01. 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 Freedom = 120 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 t .2500 .5000 .2500 .5000 .5000 -0.677 0.677 0.000 After the speed-reading course, the students scored an average of 9 words per minute higher than before they began the speed-reading course. The standard deviation of the difference scores was s = 27. 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 the t statistic. The t statistic is . Use the tool to evaluate the null hypothesis. The t statistic in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is . The cognitive psychologist conclude that the speed-reading course increases reading speed.
A cognitive psychologist is interested in whether taking a speed-reading course increases reading speed. She has students complete a reading speed test before and after a six-week speed-reading course.
In the beginning of the study, a randomly selected group of 121 students scored an average of 252 words per minute on the reading speed test. Since the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of M
D
D
is normal. She plans to use a repeated-measures t test.
The cognitive psychologist identifies the null and alternative hypotheses as:
H₀ : μ
D
D
0
H₁ : μ
D
D
0
Use the Distributions tool to find the critical region(s) for α = 0.01.
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 Freedom = 120
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
t
.2500
.5000
.2500
.5000
.5000
-0.677
0.677
0.000
After the speed-reading course, the students scored an average of 9 words per minute higher than before they began the speed-reading course. The standard deviation of the difference scores was s = 27.
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 the t statistic. The t statistic is .
Use the tool to evaluate the null hypothesis. The t statistic in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is . The cognitive psychologist conclude that the speed-reading course increases reading speed.
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