Question 3: t-test for dependent means (sometimes called "paired samples t-test") Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device put into their cars kept records of their speeds for two weeks before and after the workshop. The maximum speeds for each person during the two weeks before and two weeks after are given below. In Parts A and B, we will do a t-test for dependent means to determine if we should conclude that people change their speeds after the workshop. We will do a two-tailed test with significance level .05. Please see the document, "Lab Assignment 5 Example - t-test for dependent means" for help. First, fill in the rest of the table to get the SS | Participant | Before | After | Difference (After - Before) | Difference-M | (Difference - M)² | | :--- | :--- | :--- | :--- | :--- | :--- | | 1 | 65 | 58 | | | | | 2 | 62 | 65 | | | | | 3 | 60 | 56 | | | | | 4 | 70 | 66 | | | | | 5 | 68 | 60 | | | | | SUM | | | | 0 | | Part A. By hand, use the five steps of hypothesis testing and see if the data support your hypothesis. 1. Restate the question as a research hypothesis and a null hypothesis about the populations. 2. Determine the characteristics of the comparison distribution. 3. Determine the cutoff sample score (or critical value) on the comparison distribution at which the null hypothesis should be rejected. 4. Determine your sample's score on the comparison distribution.
Added by Bethany N.
Close
Step 1
Restate the question: Do people change their speeds after attending a workshop on speeding? Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 65 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The following data are from a completely randomized design. Treatment A Treatment B Treatment C 31 43 34 29 44 37 29 44 34 26 47 37 30 42 33 Sample mean 29 44 35 Sample variance 3.50 3.50 3.50 (a) At the α = 0.05 level of significance, can we reject the null hypothesis that the means of the three treatments are equal? State the null and alternative hypotheses. H0: Not all the population means are equal. Ha: μA = μB = μC H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: μA = μB = μC Ha: μA ≠ μB ≠ μC H0: μA ≠ μB ≠ μC Ha: μA = μB = μC H0: μA = μB = μC Ha: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal. Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal. Reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal. Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are not equal. (b) Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use α = 0.05. Find the value of LSD. (Round your answer to two decimal places.) LSD = Find the pairwise absolute difference between sample means for each pair of treatments. xA − xB = xA − xC = xB − xC = Which treatment means differ significantly? (Select all that apply.) There is a significant difference between the means for treatments A and B. There is a significant difference between the means for treatments A and C. There is a significant difference between the means for treatments B and C. There are no significant differences. (c) Use Fisher's LSD procedure to develop a 95% confidence interval estimate of the difference between the means of treatments A and B. (Use xA − xB. Round your answers to two decimal places.) to
Sheryl E.
4. Dr. Edwin Jenner conducts a study in which participants are asked to learn a list of words consisting of concrete words (e.g., zombie, brain, crossbow) and abstract words (e.g., fear, hope, safety). Dr. Jenner hypothesizes that more concrete than abstract words will be remembered. Each participant is asked to recall as many words as possible 10 minutes after presentation, and the number of concrete and abstract words each person recalls is determined. The data, along with means and standard deviations, are presented below. What do you conclude with respect to the researcher's hypothesis? [If this is an independent samples t-test problem, use non-pooled variances] Determine the appropriate test, state the null hypothesis symbolically, state the research hypothesis symbolically (being sure to determine if the alternative hypothesis should be directional or nondirectional), show the appropriate formula, your substitutions, and your obtained value, state what the critical value(s) is/are, state your decision with respect to the null hypothesis (reject the null or fail to reject the null), and state your conclusion in words, including the t statement. Example 1: Section B's average MT1 FIB score (M = 79.22, s = 12.39) was significantly higher than Section A's average (M = 75.76, s = 10.43), t(290) = -1.99, p < .05. Unless otherwise stated, assume that alpha is set at .05, and that the population is normally distributed. For independent samples t-test problems, use non-pooled variances.
Madhur L.
A teacher was interested to see if a change of curriculum/instructional approach would make a difference in student achievement - possibly at a statistically significant level. As such, the teacher assessed his students as a "Pre-Test", and after nine weeks of the new curricular/instructional approach, assessed his students in a "Post-Test" fashion. The following depicts both the "Pre-Test" and "Post-Test" achievement scores of the students enrolled in the teacher's class: Pre-Test Phase Post-Test Phase 77 85 65 71 45 70 89 90 81 85 75 75 88 89 78 83 90 90 81 84 76 86 73 77 80 86 66 75 87 90 Assignment: 1. What was the mean difference of the comparison in Pre-Test and Post-Test scores? - The mean difference of the comparison in Pre-Test and Post-Test is -5.6667. 2. What was the statistical significance level (p) of the mean score comparison? - The statistical significance level is 0.0032. 3. Was the "Assumption of Normality" satisfied with the data associated with the scenario? Provide a statistical rationale for your response... (Hint: address the Pre/Post Test Difference data)... *Note: If the assumption of normality has been violated in the scenario, merely state it with the statistical rationale in your response. The researcher would then have the option of "Bootstrapping" the finding in SPSS or use the Non-Parametric alternative to the t test of Dependent Means - the Wilcoxon Sign-Rank Test. 4. Given the finding in the scenario, does the researcher "Reject or Retain" the Null Hypothesis (H0) that would be associated with the scenario? Provide a rationale for your response... 5. If the Alternative Hypothesis (Ha) for the scenario was stated as, "The novel curricular/instructional technique will increase student achievement at a statistically significant level", what would be the researcher's response? Provide a rationale for your response...
Dominador T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD