Hypothesis Testing and T-Tests: A Step-by-Step Guide

School

University of Waterloo**We aren't endorsed by this school

Course

PSYCH 292

Subject

Statistics

Date

Dec 10, 2024

Pages

Uploaded by PrivateOxide28422

ASSIGNMENTQUESTION 1:For the following questions on hypothesis testing and t-tests (59 total marks), be sure to use the five-step process demonstrated in class and by the Tutorial Leaders. In addition, be sure to show all your work including:1)Draw and shade the distribution 2)Relevant formulas (if any)3)Rearrangement of formulas (if needed)4)Concluding statements

THE PHOTO INCLUDES QUESTION 1 STEP 1 AND STEP 21)You are conducting a study on students’ caffeine consumption. You believe that students might consume significantly more coffee during exam periods than prior to exam periods. To test this prediction, you conduct a pilot study asking a random sample of 10 students who drink coffee daily to report their average coffee consumption in March and a second (different) random sample to report their average coffee consumption in April. The results are shown in the table below.(20 marks)Step 1: State the hypotheses:Step 2: Locate the critical region:

Step 3: Compute the test statistic:

Step 4: Make a decision:Step 5: Report the result of the test: IN PHOTOa)

b)Again, use a two-tailed test and alpha = .05. (20 marks)Step 1: State the hypotheses:Step 2: Locate the critical region:Step 3: Compute the test statistic:Step 4: Make a decision:Step 5: Report the result of the test:ALL IN PHOTO BELOW

STEP 1,2,3,4,5 ALL IN PHOTO

c)Compare the outcomes of the tests in parts (a) and (b). What can you conclude about the power of dependent and independent designs? Why is this the case? (3 marks) IN PHOTOd)Calculate and compare Cohen’s dfor both the independent t-test and the dependent t-test. Why does the effect size change? (8 marks) IN SAME PHOTO

e)Calculate and compare the 95% confidence interval for the independent t-test and the dependent t-test. Why is there a difference in the intervals? (8 marks)

QUESTION 2 – Dependent & Independent t-test (10 marks)Go to LEARN and navigate to CONTENT R Activities. Complete Activity 6 – Dependent & Independent t-tests.Note that there is only a video for this activity and that you will need to download the beersand looksdata files from LEARN in addition to the video to complete the activity.Replicate the dependent and independent t-tests from Question 1 of this assignmentusing R. Copy the result of your tests from the Console pain and paste them below.View(Calendar)> march <- c(8, 10, 10, 15, 10, 20, 11, 11, 10, 25)> april <- c(10, 12, 20, 15, 20, 14, 20, 14, 20, 25)> > # Dependent t-test> dependent_t_test <- t.test(march, april, paired = TRUE)> dependent_t_testPaired t-testdata: march and aprilt = -2.2925, df = 9, p-value = 0.04758alternative hypothesis: true mean difference is not equal to 095 percent confidence interval:-7.94708793 -0.05291207sample estimates:mean difference -4 > # Independent t-test> independent_t_test <- t.test(march, april, paired = FALSE)> independent_t_testWelch Two Sample t-testdata: march and aprilt = -1.7655, df = 17.596, p-value = 0.09483alternative hypothesis: true difference in means is not equal to 095 percent confidence interval:-8.7678747 0.7678747sample estimates:mean of x mean of y 13 17

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