t-test: two independent samples and matched pairs t-test

Statistics Homework Seven (15 pt) t-test: two independent samples Note: This assignment can be done quickly if utilizing SPSS From page 138, you will read, The Student’s t ratio is used for analyses that compare two groups that are independent. In a two-sample analysis, we are drawing two samples, finding the differences between the means of each group, and obtaining a distribution of these differences. This week you will determine if there is a statistically significant difference in mean Composite ACT Second Attempt Scores between students taking ACT prep and students not taking the ACT prep. This requires calculating a t static. The independent t-test requires the researcher to check for three assumptions. These assumptions are identified on page 139 if the text. This will require you to review the variance, skew, and kurtosis calculated in HW Assignment Two. o Are the ACT Second Attempt Score variances significantly different? Explain why or why not. (3 pt). o Are the data for each group normally distributed? Explain why or why not. (3 pt) o Using the independent t-test, determine if there is a statistically significant difference in second attempt ACT scores between students who took the ACT prep and those that did not take the prep. This will require calculation of t and comparing the calculation to the t critical value table on page 184. Is there a statistically significant difference? Why is there a difference? Explain how you came to that conclusion. (9 pt) In research, we often look at samples which have been matched on some criteria or pre- post-designs in which we are looking at a single group before and after some intervention (pg. 142). A repeated measure t-test is also labelled as a dependent t-test and a matched pairs t-test. The repeated t-test is called repeated because the same measure, or variable, is recorded from a sample twice. Generally, such as in our RSH data set, the first measure occurs at time one and the second measure occurs at time two. For our data set, RSH data set, ACT first attempt score was taken at time one, and ACT second attempt score was taken at time two. The repeated measure, or variable, for our data set is Composite ACT Score. A description of the matched pairs t-test is provided in Chapter 14, page 142. For this assignment, you will determine if there is a statistically significant difference in mean Composite ACT score for students who took the ACT prep course and for students who did not take the ACT prep course. The degrees of freedom for a matched pairs t test is the number of matched pairs minus one. Using the critical values table on page 184, determine if the calculated t-statistics are greater than the critical value for a two-tailed test at an alpha level of 0.05 (95% confidence that there is a difference from pre to post ACT scores). Provide the following: Null Hypotheses (one for the group of students that did not take the ACT, a second null hypothesis for the group of students who did take the ACT prep) (2 pt). Degrees of freedom for both t-tests. (2 pt) CV for both t-tests. (2 pt). t- value for both t-tests. (10 pt) A conclusion for accepting or rejecting each null hypothesis with an explanation for why each hypothesis was accepted or rejected. (4 pt)