Question

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 B1 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 M_D is normal. He plans to use a repeated-measures t-test. The cognitive psychologist identifies the null and alternative hypothesis as: H_1: mu_o H_1: mu_o Use the Distributions tool to find the critical region(s) for alpha = .05. The critical t-store, which is the value for t-scores that separates the tall(s) from the main body of the distribution and forms the critical region(s), is ______. 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 sores was s = 22. To calculate the t statistic, you must first calculate the estimated standard error. The estimated standard error is _______. 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 increasing reading speed improves comprehension.

Answer 1

State the hypotheses. Null hypothesis: That is there is no evidence that increasing reading speed improves comprehension Alternative hypothesis That is there is evidence that increasing reading speed improves comprehension Rejection rule: If treet satistic riticalva then the null hypothesis is rejected.

Find the critical value. The degrees of freedom is n-1 81-1 -80 Thus, the critical value with 80 degrees of freedom and 0.05 level of significance from the 't distribution table for the right tail is 1.664. Calculate the standard error and the test statistic using MINITAB. MINITAB procedure: Step 1: Choose Stat> Basic Statistics > Paired t. Step 2: Choose Summarized data Step 3: Enter Sample size as 81, Mean as 4, Standard deviation as 22. Step 4: Choose Options. Step 5: In Confidence level, enter 95.0 Step 6: In Alternative, select greater than. Step 9: Click OK.

MINITAB output Paired T-Test and CI N Mean StDev SE Mean Difference 81 4.00 22.00 2.44 95% lower bound for mean difference: -0.07 T-Test of mean difference = 0 (vs > 0) : T-value = 1.64 p-value 0.053 From MINITAB output, the value of standard error is 2.44 and value of test statistic is 1.64 Conclusion: Here the test statistic v 1.64) is less than the critical value 1.66) By therejection rule, do not reject the null hypothesis. Therefore, it can be concluded that, there is no evidence that increasing reading speed mproves comprehension