Please only answer if you can complete and answer each section!! 8. A one-tailed
ID: 3181010 • Letter: P
Question
Please only answer if you can complete and answer each section!!
8. A one-tailed hypothesis test for a repeated-measures design Aa Aa A researcher is interested in whether using your finger to follow the words you are reading decreases reading speed. She has students complete a reading speed test, first without using their fingers to follow the words, and then again while using their fingers to follow the words. In the beginning of the study, a randomly selected group of 49 students scored an average of 248 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. She 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 a .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.)Explanation / 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 0.01. 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 = 33 (Given)
SE = s / sqrt(n)
S.E = 4.714
DF = n - 1 = 49 -1
D.F = 48
t = [ (x1 - x2) - D ] / SE
t = 1.273
tcritical = 2.407
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 two-tailed test, the P-value is the probability that a t statistic having 48 degrees of freedom is greater than 1.273
We use the t Distribution Calculator to find P(t > 1.273) = 0.105
Interpret results. Since the P-value (0.105) is greater than the significance level (0.01), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence that using your fingers to follow the words you are reading decrease the words.