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ID: 3244639 • Letter: M
Question
MindTap-Cengage Learning d ng.cengage.com/static/nb/ui/index.html?nbld-559647&nbNodeld-20227863A;&elSBN-9781; 30564 7305#1&parentid;=202278723 Apps MINDTAP Charles Gyamfi Charles Gyamfi, (?) The t Test for Two Related Samples -Aplia Due Tomorrow at 1 1 PM EDT Back to Assignment Attempts: Keep the Highest: 8 5. A one-tailed hypothesis test for a repeated-measures design Aa Aa A researcher is interested in whether blind Braille readers could be taught to read faster using the same techniques as sighted readers. He has blind adults complete a reading speed test before and after a six-week speed-reading course A-Z In the beginning of the study, a randomly selected group of 121 blind Braille readers scored an average of 261 words per minute on the reading speed test. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of Mp is normal. He plans to use a repeated-measures t-test. The researcher identifies the null and alternative hypotheses as: Use the Distributions tool to find the critical region (s) for -.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 consider whether this is a one-tailed or two-tailed test.) (Hint: Remember to set the degrees of freedom on the tool and toExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: d< 0
Alternative hypothesis: d > 0
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t).
s = sqrt [ ((di - d)2 / (n - 1) ]
s = 21
SE = s / sqrt(n)
S.E = 1.91
DF = n - 1 = 121 - 1
D.F = 120
t = [ (x1 - x2) - D ] / SE
t = 3.66
tcritical = 1.658
Rejection or critical region = t > 1.658
where di is the observed difference for pair i, d is mean difference between sample pairs, D is the hypothesized mean difference between population pairs, and n is the number of pairs.
Interpret results. Since the t statistics lies in rejection region, hence we have to reject the null hypothesis.
The researcher can conclude that the speed course increases the speed of reading Braille.