Lab 4

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Purdue University *

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301

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Statistics

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Apr 3, 2024

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Lilyhan Liao Yaxin Fang Dr. Munson Lab 4: Matched Pairs and 2 Sample Comparison of Means T-tests 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). 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). Question 1: Whether the population mean sleep time during weekday (Sleep_time_week) is different depending on gender of subjects. Question 2: Whether for the population, sleep time during weekend (Sleep_time_weekend) is greater than the sleep 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. 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 use matched pairs with question 2. Matched pairs are typically used on two sets of measurements on the same subjects but under different conditions. Pertaining to this case, because we have data for the same subjects comparing their sleep times on weekdays to weekends, we can use matched pairs to analyze the difference in sleep times in the two categories for each subject individually. In terms of data set, I would use (a) because it gives me the sleep times for each subject on the weekdays and the weekends. 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"). HO= μ diff =0 HA= μ diff> 0 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”). SPSS Output Below Paired Samples Statistics Pair 1 Mean N Std. Deviation Std. Error Mean Sleep time week 6.9966 150 .51708 .04222 Sleep time weekend 7.9681 150 1.16024 .09473

Paired Samples Test Pair 1 Sleep time week Sleep time weekend Mean SD SD Error Mean Lower Upper t df One sided p Two sided p -.97147 1.0 049 8 .0820 6 - 1.1336 1 - .80932 - 11.8 39 14 9 <.001 <.001 a. What are the individual means for the two lists of data? Sleep time week mean: 7.000 hours Sleep time weekend mean: 7.968 hours b. What is the SAMPLE mean difference? Sample mean difference: -0.971 c. What is the 95% confidence interval for the POPULATION mean difference? Round your answer to 4 decimal places, otherwise only partial credit will be given. (-1.1336, -0.8093) d. 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 2? Test statistic: -11.839 Probability statement: P value= P (t> -11.839) P-value: less than 0.001 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. 0.001< 0.05 Reject null because the p value is less than alpha. This means that we have evidence that the subjects have a greater sleep time on the weekend compared to the weekday. My conclusion refers to the population. 3. (1 point) For which of the questions on the first page would you use a Two-Sample Comparison of Means to answer, (1) or (2)? Which dataset can be used to answer that question, (a) or (b)? How do you know? I would use question 1 for a two-sample comparison of means. This is because the question is asking about determining whether the population mean sleep time during weekdays is any different depending on the gender of subjects. This is addressed with a two-sample comparison of means because a subject's sleep time during weekdays is a completely different category to gender. They’re two completely different groups. Data set (b) corresponds to this question because it gives each subject's sleep time during the week and their gender.

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4. Analyze the data from the two-sample comparison of means question in SPSS using the appropriate statistical method of inference. Do not assume equal variances. (Notes: USE Gender as the “Grouping Variable” and define groups as “male” and “female”. Make sure you include all SPSS output in your Brightspace submission. The variable to analyze is Sleep_time_week). SPSS Output Below Group statistics Gender N Mean SD Standard Error Mean Sleep time week male 76 6.9784 0.52018 0.05967 female 74 7.0153 0.51675 0.06007 Independent Samples Test Sleep Time week Equal varia nces assu med F Sig t df One side d P Two sided P Mean Differ ence STD Error Diffe rence Low er Uppe r Equal varia nces not assu med 0.002 0.965 - 0.435 148 0.32 2 0.664 - 0.036 85 0.084 68 - 0.20 418 0.13 048 - 0.435 147.93 9 0.32 2 0.664 - 0.036 85 0.084 67 - 0.20 417 0.13 047 a. What are your hypotheses? (Define the order you are using for the difference between the parameters (e.g. " parameter 1" - " parameter 2"). H0: μw=μm HA : µw≠µm b. Answer all the questions below. What are the individual means for the two lists of data? Male mean: 6.978 Female mean: 7.015 What is the difference in the SAMPLE means? -0.037 c. 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.

(-0.204, 0.130) d. 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? Test statistic: -0.435 Probability statement: P value= P (t ≠ -0.435) P value= 0.664 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. 0.664> 0.05 Because the p value is greater than alpha, we will fail to reject the null. We don’t have enough evidence to conclude that the population’s mean sleep time during the weekdays is significantly different from their corresponding genders. This conclusion refers to the population.

Lab 4

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