Statistics questions. Please help me. This is so hard for me 6. A one-tailed hyp
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Question
Statistics questions. Please help me. This is so hard for me
6. A one-tailed hypothesis test for a repeated-measures design Aa Aa E 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. 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 MD is normal. He plans to use a repeated-measures t-test. The researcher identifies the nu and alternative hypotheses as Ho: HD H1: HD Use the Distributions tool to find the critical region(s) for o 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 of freedom on the tool and to consider whether this is a one-tailed or two-tailed test.) t Distribution Degrees of Freedom 115 5000 5000Explanation / 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(Given)
SE = s / sqrt(n)
S.E = 1.91
DF = n - 1 = 121 -1
D.F = 120
t = [ (x1 - x2) - D ] / SE
t = 3.665
tcritical = 1.658
Critical region is 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.
Since we have a one-tailed test, the P-value is the probability that a t statistic having 120 degrees of freedom is more extreme than 3.665
We use the t Distribution Calculator to find and P(t > 3.665) = 0.0002
Interpret results. Since the P-value (0.0002) is less than the significance level (0.05), we have to reject the null hypothesis.
The researcher have sufficient evidence to conclude that speed reading course increases speed of reading Braille.