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DATA SELECT CASESI found that the bigger the sample size got, the closer the means were to each other.INTRODUCTORY STATSTICS STATS 101Sampling from a Larger Population Name: Yosef Tropper Lab 2 In this laboratory we will draw samples of different sizes from the data for our class and then look at statistics calculated on those samples. We will be working with the variable Weight using the “Lab02 – Data.sav” file. 1. Get the statistics for Weight for the whole population. In this case, our class (plus the class from the Fall semester) constitutes the population. Use DESCRIPTIVES (Analyze Descriptive Statistics Descriptives), place Weight in the variable box, click on Options, select “mean” and “std deviation”, click Continue and then OK. Please list the mean and standard deviation for thepopulation below. Mean: 151.10 S.D.: 46.272. Now, we are going to draw samples of 5 people at random from the 100 people in the whole data set (note: only 126 people have values for Weight). To do this, follow these menu selections:DATA SELECT CASESIn SELECT CASES, click the small button for Random sample of cases, then click the button under that for SAMPLE. In the dialog box, indicate that you wantto sampleExactly 5 cases from the first 100 casesThen click CONTINUE and then OK. These steps will have randomly selected 5 out of the 100 people; that is, you will have drawn a sample of 5 from the population of 100 (actually the population is 126 people – see note above).Now, use DESCRIPTIVES to find the Mean, Standard Deviation, and S.E. of the Mean (standard error of the mean) for this sample. Click on OPTIONS in DESCRIPTIVES to choose the desired statistics (note: this is the same procedure as in #1 above except you are simply requesting one additional statistic – the standard error of the mean). The Standard Error of the Mean is the standard deviation of the distribution of the sample means for samples of size 5. The output is a little confusing. You will see a column with the N (number of cases), the Mean, the Std. Error (standard error of the mean), and the Std. Statistic (standard deviation). Please write the values you obtained below. Sample 1: Mean 161.58 S.D. 53.80 S.E. 24.06Now, continuing on the back of this page, repeat the entire process four more times: Go back to SELECT CASES and click OK to get a new sample of 5 people. Then go to DESCRIPTIVES and get the statistics for the new sample.Sample 2: Mean 182.85 S.D. 46.80 S.E. 20.93Sample 3: Mean 196.93 S.D. 39.44 S.E. 17.64Sample 4: Mean 165.10 S.D. 43.90 S.E. 19.63Sample 5: Mean 112.43 S.D. 50.08 S.E. 22.40_3. Now repeat that entire process, but this time, select samples of size 10.Sample 1: Mean 167.56 S.D. 40.99 S.E. 12.96Sample 2: Mean 155.88 S.D. 45.38 S.E. 14.35Sample 3: Mean 156.19 S.D. 45.03 S.E. 14.24Sample 4: Mean 153.32 S.D. 38.28 S.E. 12.11Sample 5: Mean 176.98 S.D. 50.24 S.E. 15.894. Now, one last time. Do it again, but this time, select samples of size 50.Sample 1: Mean 148.59 S.D. 34.39 S.E. 4.86Sample 2: Mean 150.51 S.D. 54.37 S.E. 7.69Sample 3: Mean 155.64 S.D. 47.46 S.E. 6.71Sample 4: Mean 154.91 S.D. 46.73 S.E. 6.61Sample 5: Mean 156.82 S.D. 45.68 S.E. 6.465. Now, one last time. Do it again, but this time, select samples of size 75.Sample 1: Mean 148.93 S.D. 42.10 S.E. 4.86Sample 2: Mean 149.98 S.D. 47.91 S.E. 5.53Sample 3: Mean 151.03 S.D. 46.96 S.E. 5.42Sample 4: Mean 154.67 S.D. 45.40 S.E. 5.24Sample 5: Mean 152.20 S.D. 47.51 S.E. 5.496. Finally, it’s time for some conclusions. Look back over your results.a) What happened to the means as the sample size got larger? Did they change in any systematic way relative to the overall mean for all 100 people (the whole population)?I found that the bigger the sample size got, the closer the means were to each other.What happened to the standard deviations as the sample size got larger? Did they change in any systematic way relative to the overall mean for all 100 people (the whole population)?I found that as the sample size got larger, there was no meaningful effect on the standard deviations.What happened to the standard errors of the mean (S.E. of the mean) as the sample size got larger? Why did this happen?I found that as the sample size got larger, the standard errors of the mean got smaller. I believe that this is because bigger sample sizes are more accurate than smaller

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