Lab 4-Matched Pairs and 2 Sample Comparison of Means_blank

Name: Connor Wood T.A. name: Ziyi Wang Lab 4: Matched Pairs and 2 Sample Comparison of Means T-tests NOTE: SPSS outputs are necessary to show full completion of the lab. Please paste all SPSS outputs into your lab report and submit the completed reports including all requested tables and graphs via Brightspace (under the "Lab" folder) by 11:50 pm Friday. Two points will be deducted for each SPSS requested output that is not included in the submitted lab document. Also, 30% points will be deducted for late submission, up to 24 hours. Dataset : This lab uses the dataset ( SleepPatterns ), located on Brightspace under Lab in the Datasets submodule. Instructions for opening the dataset in SPSS are found as follows.  SPSS installed on a computer: Reference page 4 of the SPSS Instruction Manual  SPSS running remotely: Reference the slide “Opening your Dataset Remotely in SPSS via Go Remote” in the document “SPSS using Citrix access guidelines” on Brightspace. Two hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health. When you have multiple columns of data, sometimes it can be tricky to tell the difference between a Matched Pairs and a 2-Sample Comparison of Means problem. Here’s how you know: Matched pairs : You get 2 measurements on the same unit (for example, before and after measurements or left- hand vs. right hand for everyone) OR you have measurements on two sets of units, with each individual of one set being paired off (matched by some trait) with an individual of the other set. We will measure the difference between each pair, and on only ONE MEAN , the mean of these differences. 2-Sample Comparison of Means : You have 2 separate populations from which you get 2 independent samples, and you just measure each unit once (for example, men vs. women, or undergraduates vs. graduates), i.e. there are TWO MEANS and there is no valid reason to pair up the subjects. Open your lab dataset in SPSS. Below you will find a description of the variables used in this lab. Sleep_time_week: Sleep time during the week. Sleep_time_weekend: Sleep time during the weekend. Gender: Gender of subject (female, male).

Check the dataset variables description on Brightspace if you would like more details on the variables. This dataset contains information for 250 subjects. We are interested in the following from this dataset: (a) For each subject we have measurements of the sleep time during weekday ( Sleep_time_week ) and during weekend ( Sleep_time_weekend ). (b) For all the 250 subjects, the researchers recorded their Gender , and recorded their sleep time during weekday ( Sleep_time_week) . There are two types of questions we can pose based on the two sets of data described in (a) and (b). We want to know: (1) Whether the population mean sleep time during weekday ( Sleep_time_week ) is different depending on gender of subjects (Gender). (2) Whether for the population, sleep time during weekend ( Sleep_time_weekend) is greater than the sleep time during weekday ( Sleep_time_week ), or whether the mean difference between Sleep_time_weekend and Sleep_time_week is positive. The following lab will refer to these data ((a) and (b)) and questions ((1) and (2)). The lab begins below.  PAGES 12-14 IN THE SPSS INSTRUCTION MANUAL WILL ONCE AGAIN BE OF CONSIDERABLE USE TO YOU.  ROUND YOUR ANSWERS TO 3 DECIMAL PLACES. 1. (1 point) For which of the above questions would you use Matched Pairs to answer, (1) or (2)? Which dataset can be used to answer that question, (a) or (b)? How do you know? I would choose 2 which would answer a. I know because matched pairs are usually used to separate groups. 2. For the question selected as a Matched Pairs case, analyze the dataset in SPSS using the appropriate statistical method of inference. Use α = 0.05. Note: Make sure you include all output used for the following inferential procedures in your Brightspace submission. a. (2 points) What are your hypotheses? (Define the order you are using for the difference between the parameters (e.g. " parameter 1 " - " parameter 2 "). H o : μ 1 =μ 2 1 = Sleep_time_weekend H a : μ 1 >μ 2 2= Sleep_time _week b. (2 points) Answer all the questions below. (Notes: (i) running the matched pairs test in SPSS will give you all the relevant output; (ii) to make the table/output fit on a page in Word, right click in it, then click on “AutoFit -> AutoFit to Contents”). Paired Samples Test Paired Differences t df Significanc e Mean Std. Deviatio n Std. Error Mean 95% Confidence Interval of the Difference One- Side d p Two- Side d p

Independent Samples Test Levene' s Test for Equality of Varianc es t-test for Equality of Means F Sig . t df Significan ce Mean Differen ce Std. Error Differen ce 95% Confidence Interval of the Difference One - Side d p Two - Side d p Lowe r Uppe r Sleep_time_w eek Equal varianc es assume d .56 2 .45 4 1.11 2 248 .134 .267 .06417 .05772 -.049 51 .1778 4 Equal varianc es not assume d 1.11 1 245.8 57 .134 .268 .06417 .05775 -.049 58 .1779 2 a. (2 points) What are your hypotheses? (Define the order you are using for the difference between the parameters (e.g. " parameter 1 " - " parameter 2 "). H o : μ male - μ female = 0 H a : μ male - μ female ≠ 0 b. (2 points) Answer all the questions below. What are the individual means for the two lists of data? Male: 7.0766 Female: 7.0124 What is the difference in the SAMPLE means ? 0.06417 c. (1 point) What is the 95% confidence interval for the difference of the means? Round your answer to 3 decimal places, otherwise only partial credit will be given.

(0.050, 0.178) d. (2 points) What are your (i) test statistic, (ii) probability statement for the test statistic and (iii) p-value corresponding to the hypothesis test in part (a) of question 4? i. t = 1.111 ii. p-value = (T>1.111) iii. p-value = 0.134 e. (2 points) What is your conclusion in terms of the story ? Use a 5% significance level . Make sure to specify whether your conclusion refers to the population or the sample . 0.134>0.05 We fail to reject H 0 . There is not enough evidence to conclude that the population mean of Sleep_time_week is different depending on gender of subjects.