(these variables are from another data source, they are not available in the data you are using) One-Sample T-test 1. Variable: Number of Hours Worked Last Week (hrs1) The variable I chose to analyze comes from the 2008 GSS and is called \"hrs1,\" or \"number of hours worked last week.\" This variable measures how many hours respondents (a representative sample of US citizens) worked in the week prior to being surveyed. I think that number of hours worked in a week is appropriately measured at an interval/ratio level (that is, the distance between each category is equidistant) and will be suitable for t-testing because it is measure this way. It appears here that US residents work, on average, 42 hours per week; however the median and mode indicate 40 hours, so there are people who are working many more than 40 a week. I can see that the highest reported time is 89 -- so some people are working more than full-time hours. The standard deviation is REALLY high so we can tell there is a lot of difference in the amount of weekly hours worked in this sample. According to the Bureau of Labor Statistics, this is typical, though there is some fluctuation based on gender and full/part time status. SOURCE: http://www.bls.gov/opub/ted/2015/time-spentworking-by-full-and-part-time-status-gender-and-location-in-2014.htm (Links to an external site.). N=744 mean: 42 median: 40 mode: 40 standard deviation: 14.48 standard error: .417 minimum value: 1 maximum value: 89 range: 88 2. Hypotheses My null hypothesis is that there is no statistically significant difference between the mean \"number of hours worked last week\" and a \"typical\" 40-hour work week. My research hypothesis is that there is a statistically significant difference between the mean \"number of hours worked last week\" and a 40-hour work week. In the United States, a full-time job is traditionally equated with a 40-hour work week. However, the mean number of hours worked by 2008 GSS respondents in the week prior to being surveyed was 42 hours. I am interested in finding out whether this difference is statistically significant, or whether the difference can be attributed to sampling error. 3. One-Sample t-test statistics: mean difference: 2.003 degrees of freedom: 1202 obtained t-statistic: 4.799 t-critical: +/- 1.960 p-value: 0.000 4. Decision based on hypotheses: Is this a significant mean difference in your variable? Report your decision as whether you accept or reject the null hypothesis and why you came to this decision. (1-2 sentences). We are evaluating your ability to read, interpret, and report findings from statistical tests. 5. Results and Reflection: In addition to a description of the type of statistical test performed here, explain these measures you have now obtained and reported and explain what they mean (2-3 sentences). Explain your results in a 'real world' context. My analysis shows that despite the rather small practical difference between the mean \"number of hours worked last week\" and a \"typical\" 40-hour work week (2.003 hours), that this difference is nevertheless statistically significant. We thus have sufficient evidence to conclude that the number of hours worked per week in 2008 were significantly higher than the \"typical\" 40hour work week and the difference is significant at the .05 level. I wonder why people in my survey worked more hours than a typical workweek! Independent Samples T-tests For Part 2, I will examine whether there is mean difference in poor mental health days by age group and by gender. 6. Variable Information: For my tests, I selected poor mental health (over the past month; measured at an interval-ratio level), gender (a dichotomous sorting variable), and age group (a dichotomous sorting variable separating people into two age groups). Poor Mental health days is ideally measured at an interval-ratio level because each day is equidistant from the other. The variable may not fully tap a person's actual mental health because they may have had a major sad life event rather than be in poor mental health. I elected to look at age and gender differences in mental health because there is a lot of literature about these issues. Often, older people may suffer mental health declines due to social isolation and depression due to a reduction in social obligations (i.e., role loss). When it comes to gender, women and men may have similar rates of mental illness; however women may report or experience more depression than their men counterparts, who tend to externalize in the form of antisocial behavior. It looks like the typical person in the sample will report one poor mental health day; however the average is 3.79, so there are some people who suffer more than 20 days a month (skewing the data). This observation is confirmed because I can see that the standard deviation is over 6 days and the range is the maximum amount (i.e., 30 days). The sample is 51% man-identified which is a little different than the actual representation of men in the population, but that shouldn't affect our results much. 54% of the sample is 40 or older. SOURCE: https://www.cdc.gov/aging/pdf/mental_health.pdf (Links to an external site.) SOURCE: http://apps.who.int/iris/bitstream/10665/68884/1/a85573.pdf (Links to an external site.) Number of days in the past month in poor mental health o N=744 o Mean: 3.79 o Median: 1.00 o Mode: 0 o Standard Deviation: 6.481 o Minimum: 0 o Maximum: 30 o Range: 30 o SE: 0.238 Gender o N=744 o Mean: N/A o Median: N/A o Mode: 1 (man) o Standard Deviation: N/A o Minimum: N/A o Maximum: N/A o Range: N/A o SE: N/A Age group o N=744 o Mean: N/A o Median: N/A o Mode: 2 (40 and higher) o Standard Deviation: N/A o Minimum: N/A o Maximum: N/A o Range: N/A o SE: N/A 7. Grouping variable information: It appears here that, as I kind of expected, women report more poor mental health days in the past month than men by one day. The standard deviations are still quite high for each group, so I expect there to be similar variation in each grouping. Turning to age group, people under 40 report a lower average than people 40 and over; however the mean difference is only slightly lower. I do not anticipate the difference to be significant. Group 1: Men (they are coded "1" in the data) o Mean days of poor mental health in past month: 3.43 o Standard Deviation: 6.314 o Standard Error of Mean: .321 Group 2: Women (they are coded "2" in the data) o Mean days of poor mental health in past month:: 4.18 o Standard Deviation: 6.644 o Standard Error: .351 Group 1: Under 40 (they are coded "1" in the data) o Mean days of poor mental health in past month: 3.43 o Standard Deviation: 6.293 o Standard Error of Mean: .344 Group 2: 40 and Over (they are coded "2" in the data) o Mean days of poor mental health in past month: 3.87 o Standard Deviation: 6.639 o Standard Error: .328 8. Hypotheses Gender differences: My null hypothesis states that there is not a statistically significant difference in the mean days of poor mental health between women and men. My research hypothesis is that there is a statistically significant difference in the mean days of poor mental health between women and men. Age differences: My null hypothesis states that there is not a statistically significant difference in the mean days of poor mental health between people under 40 and people 40 and older. My research hypothesis is that there is a statistically significant difference in the mean days of poor mental health between people under 40 and people 40 and older. 9. T-test Information: BY GENDER: o Mean Difference: -.752 o Std. Error of the difference: .475 o Obtained t-statistic: -1.582 (So close -- but not beyond my critical region!) o Degrees of Freedom: 742 o t-critical: +/- 1.960 (I had to use Appendix B!) o p-value: < .0001 BY AGE: o Mean Difference: -.175 o Std. Error of the difference: .478 o Obtained t-statistic: -.366 (Not even close) o Degrees of Freedom: 742 o t-critical: +/- 1.960 (I had to use Appendix B!) o p-value: < .714 10. Decisions based on hypotheses: State your decision regarding both sets of your hypotheses tests using proper statistical language and why you made this decision (1-2 sentences each). 11. Results and Reflection: Additionally, include a discussion on the type of test you performed and the statistics obtained (i.e., mean difference, critical t, p-value, etc.) (3-4 sentences). What do these measures mean? What does your interpretation say about this sample and how do you think this reflects patterns in the population?. In a full paragraph, you should consider the following questions: Are your variables measured in the best way possible? What do the results of your tests indicate? What do your statistical findings say about the populations they represent (i.e., inference) (HINT: I list which countries we may compare our data in the codebook)? (these variables are from another data source, they are not available in the data you are using) One-Sample T-test 1. Variable: importance of owning your home Report your variable name, sample size (the "n") its mean, median, mode, standard deviation, standard error, the minimum value, the maximum value, and the range. In 3-4 sentences, critically reflect on the best measures of central tendency and variability for this data as well as what they mean N= 38574 mean: 9.0481 median: 10.00 mode: 10.00 standard deviation: 1.58330 standard error: .00806 minimum value: .00 maximum value: 10.00 range: 10.00 2. Hypotheses My null hypothesis is that 3. One-Sample t-test statistics: mean difference: 9.04809 degrees of freedom: 38573 obtained t-statistic: 1122.386 t-critical: +/- 1.960 p-value: 0.000 4. Decision based on hypotheses: Is this a significant mean difference in your variable? Report your decision as whether you accept or reject the null hypothesis and why you came to this decision. (1-2 sentences). 5. Results and Reflection: In addition to a description of the type of statistical test performed here, explain these measures you have now obtained and reported and explain what they mean (2-3 sentences). Independent Samples T-tests For Part 2, I will examine 6. Variable Information: Satisfaction with standard of living, Gender, age under 40, Satisfaction with standard of living: o N=37583 o Mean: 6.4401 o Median: 7.0 o Mode: 7.0 o Standard Dev7.0iation: 2.36008 o Minimum: 00.00 o Maximum: 10.00 o Range: 10.00 o SE: .01217 Gender o N= 18503 o Mean: n/a o Median: n/a o Mode: 1 (man) o Standard Deviation: n/a o Minimum: n/a o Maximum: n/a o Range: n/a o SE: n/a Age Group o N=16275 o Mean: n/a o Median: n/a o Mode: 2 ( above 40) o Standard Deviation: n/a o Minimum: n/a o Maximum: n/a o Range: n/a o SE: n/a The goal of independent samples t-tests are to assess how two different groups vary on one (grouping) variable. Here, I'd like you to report the initial mean differences, report the mean, standard deviation, and standard error of the mean of your chosen variable using both grouping variables (two sets of numbers expected here). Compose a short paragraph describing what you observe. 7. Grouping variable information: Group 1: Men (they are coded "1" in the data) o Mean: 6.3925 o Standard Deviation: 2.35242 o Standard Error of Mean: .01729 Group 2: Women (they are coded "2" in the data) o Mean: 6.4864 o Standard Deviation: 2.36663 o Standard Error:.01713 Group 1: Under 40 (they are coded "1" in the data) o Mean: 6.4935 o Standard Deviation: 2.33222 o Standard Error of Mean: .01598 Group 2: 40 and Over (they are coded "2" in the data) o Mean: 6.3703 o Standard Deviation: 2.39434 o Standard Error: .01877 8. Hypotheses Gender differences: My null hypothesis states that Age differences: My null hypothesis states that 9. T-test Information: BY GENDER: o Mean Difference: -.09390 o Std. Error of the difference: .02435 o Obtained t-statistic: -3.857 o Degrees of Freedom: 37581 o t-critical: +/- 1.960 o p-value: < 0.000 BY AGE: o Mean Difference: .12326 o Std. Error of the difference: .02456 o Obtained t-statistic: 5.019 o Degrees of Freedom: 37581 o t-critical: +/- 1.960 o p-value: < 0.000 10. Decisions based on hypotheses: State your decision regarding both sets of your hypotheses tests using proper statistical language and why you made this decision (1-2 sentences each). 11. Results and Reflection: Additionally, include a discussion on the type of test you performed and the statistics obtained (i.e., mean difference, critical t, p-value, etc.) (3-4 sentences). What do these measures mean? What does your interpretation say about this sample and how do you think this reflects patterns in the population?. In a full paragraph, you should consider the following questions: Are your variables measured in the best way possible? What do the results of your tests indicate? What do your statistical findings say about the populations they represent