HW6 Random Sample(2)

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Central Michigan University *

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200

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Statistics

Date

May 28, 2024

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pdf

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Uploaded by lindaya2020

HW 6: Selecting a Random Sample Directions: For homework, you will repeat the demonstration we did in class. However, this time you will be using the GSS-A dataset and different variables. 1. Repeat the exercise and select 25%, 50%, 75% and 100% of samples, as well as request descriptive ’ s for MAEDUC and PAEDUC. Select the mean, standard deviation, minimum, maximum and S.E. MEAN for each variable and each random sample. Address the questions below. a. Provide the descriptive boxes for MAEDUC and PAEDUC for 25%, 50%, 75% and 100%. Label each accordingly. 25% 50% 75%

100% b. Summarize and compare the mean and standard error at each level (25%, 50%, 75% and 100%). 25%; The mean highest level of education completed by mothers is a little lower than the mean highest level of education completed by fathers which is 11.86. The standard error in this case suggests the average for mothers is close while fathers are not as close to the true average. 50%; given the mean for both mothers and fathers, it appears that the standard error seems to be off for both parents by a bit more than at 25% 75%; at 75% mothers were 11.84 for the highest level of education and fathers 11.93. It's a little obvious we see a trend that father's typical highest level of completion is not as confident as mothers. While we might be a little uncertain about mothers, fathers are seen to be less confident. 100%; at 100% mothers' highest level of completion was 11.85while fathers are at 11.86. Both standard errors of .105 and .128 indicate that we are not as certain how accurate these numbers are, however, the standard error of .128 makes us think that the HLOE completed is quite accurate. c. What can you say about the accuracy of your random samples? How does this relate to the central limit theorem? The central limit theorem suggests that as the sample size increases, the mean has a normal distribution. Additionally, bigger sample sizes lead to decreases in the mean, therefore making the data more accurate. In this case we see that the valid population is 1015 and as we use various levels of the sample the means decrease. Mothers seem to be the most accurate throughout the data as the mean statistic was always less than fathers.

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