Answer Happy

Instructions. When answering each question, please make sure to include relevant math- ematical justification (aimed at the statistically-inclined reader) as well as a common sense interpretation tailored to the general audience. 1. You already know that the population is that of years, and the spreadsheet you chose represents a sample summarizing data about a specific country. Looking at the data, do you think that the sample was taken using the SRS (simple random sampling) technique? Please explain 2. Calculate the p-value associated with the hypothesis testing problem about the difference between the two sub-groups (either male/female or urban/rural, depending on which dataset you chose): Ho : difference = 0 Vs Ho difference 0. Based on your calculations, do you think there is evidence to support the claim that there is going to be a difference between the two categories in 2023? Hint: It does not matter what the variable of interest is called or how we constructed it. We can use the same techniques when working with sample mean of any variable be it an absolute value, or a difference between other variables. Just focus on one column. and work with it as if there were no other columns in the table. 3. Reflection. Try to think about this project outside the context of statistics. Think about the bigger picture. Specifics aside, reflect on what these data mean to you. Do you think this project affected your view/understanding of the world in any way? P.S. Please be honest, and do take some time thinking about it. The effort is all that counts for this question Bonus questions. 1. Construct a 95%-confidence interval for the expected difference between the two sub- groups. Explain what it means, and how you interpret it. List all your assumptions, as well as any concerns you might have regarding your conclusion. 2. Would it make sense to construct confidence intervals for individual sub-group values (rather than for the difference), and then compare the two confidence intervals to see if they overlap? Explain why, or why not.

1960 Year Male, yeanFemale ye Dienos - Mars 1980 65 90 7054 4.64 1961 86.27 70.94 1962 66.60 71.30 4.89 1983 68.87 7161 4.74 1964 67.00 71.30 4.30 1905 6726 72.14 488 1960 67.42 7230 4.96 1967 67.59 7254 5.05 67.81 72.93 5.12 1969 68.06 73.24 5.18 1970 68.35 73.59 5.24 1971 68.65 7393 5.28 1972 68.94 7427 5.33 1973 69.19 74.57 5.38 1974 09.41 7485 5.44 1975 69.60 75.12 5.52 1970 69.78 75 39 5.61 1977 69.97 75.70 5.73 1978 70.17 7803 5.86 1979 70.40 78.40 6.00 1930 70.65 76.79 6.14 1981 70.91 77.18 6.27 1982 71.16 77.56 6.40 1983 71.40 77.69 6.49 1984 71.63 78.18 6.55 1985 71.88 78.44 6.56 1966 72.16 78,66 6.50 1987 7248 78.87 6.38 1988 79.07 6.21 1989 74.20 79.30 5.10 74.50 79.50 1991 74.60 79.80 5.20 74.70 80.20 5.50 1993 75.00 79.90 490 1994 7520 80.20 5.00 1995 75.00 80.30 5.30 1996 75.10 80.40 5.30 1997 75 60 80.80 5.20 1998 75.40 80.40 5.00 1999 75.50 80 80 5.10 2000 75.40 30.50 5.10 2001 75.90 81.00 5.10 2002 78.30 81.10 4.30 2003 76.50 81.30 4.80 78.60 81.60 5.00 2005 78.80 81.80 5.00 2000 77.00 82.00 5.00 2007 77.00 B2.00 5.00 2000 77 50 8250 5.00 2009 77.70 82.80 5.10 77.90 B3.00 5.10 2011 78.00 83.60 5.60 2012 78.00 83.40 5.40 2013 78.70 14.00 5.30 2014 78.80 84.10 5.30 2015 78.50 83.70 5.20 2016 78.90 34.00 5.10 2017 78.80 83.90 5.10 2018 79.30 84.40 5.10 72 88 1990 5.00 1992 2004 2010 Mean Sid. dov Q1 Q2 Os IOR (55) IOR 73.03 4.08 66.51 74.20 76.55 7.04 10.57 78.38 4.07 7490 79,30 81.45 6.46 9.70 5.34 0.53 5.00 5.18 5.51 051 0.76

VS Instructions. When answering each question, please make sure to include relevant math- ematical justification (aimed at the statistically-inclined reader) as well as a common sense interpretation tailored to the general audience. 1. You already know that the population is that of years, and the spreadsheet you chose represents a sample summarizing data about a specific country. Looking at the data, do you think that the sample was taken using the SRS (simple random sampling) technique? Please explain. 2. Calculate the p-value associated with the hypothesis testing problem about the difference between the two sub-groups (either male/female or urban/rural, depending on which dataset you chose): Ho difference = 0 Ho difference +0. Based on your calculations, do you think there is evidence to support the claim that there is going to be a difference between the two categories in 2023? Hint: It does not matter what the variable of interest is called or how we constructed it. We can use the same techniques when working with sample mean of any variable be it an absolute value, or a difference between other variables. Just focus on one column, and work with it as if there were no other columns in the table. 3. Reflection. Try to think about this project outside the context of statistics. Think about the bigger picture. Specifics aside, reflect on what these data mean to you. Do you think this project affected your view/understanding of the world in any way? P.S. Please be honest, and do take some time thinking about it. The effort is all that counts for this question. Bonus questions. 1. Construct a 95%-confidence interval for the expected difference between the two sub- groups. Explain what it means, and how you interpret it. List all your assumptions, as well as any concerns you might have regarding your conclusion 2. Would it make sense to construct confidence intervals for individual sub-group values (rather than for the difference), and then compare the two confidence intervals to see if they overlap? Explain why, or why not.

5.61 Year Male, yeah Female, yerference ( FM) years 1960 65.00 TO 54 4.64 1901 66 27 70.94 4.66 1062 66.60 7130 4.69 1903 66.87 71.81 4.74 1964 67.09 71.89 4.80 1965 67.26 72.14 4.88 1966 67.42 7238 1967 67.59 7254 5.05 1968 67.81 72.93 5.12 1969 68.06 73.24 5.18 1970 68.35 73.59 5.24 1971 68.65 73.93 5.28 1972 68.94 7427 5.33 1973 69.19 74 57 5.38 1974 69.41 74 85 5.44 1975 89.60 75.12 5.52 1976 69.78 75.39 1977 69.97 75.70 5.73 1978 70.17 76.03 5.86 1979 70.40 76.40 6.00 1980 70.65 76.79 6.14 1981 70.91 77.18 6.27 1962 71.16 77.56 6.40 1983 71.40 77 89 6.49 1984 71.63 78.18 6.55 1985 71.88 78.44 8.56 1995 72.16 78,66 6.50 1987 72.48 78 87 5.38 1988 72.66 79.07 6.21 1989 74.20 79.30 5.10 1990 74.50 79,50 5.00 1991 74.00 79 80 5.20 1992 74.70 80.20 5.50 1993 75.00 79.90 4.90 1994 75.20 80.20 5.00 1995 75.00 80.30 5.30 1996 75.10 80.40 1997 75.60 80.80 5.20 1990 75.40 80.40 5.00 1999 75.50 80.50 5.10 2000 75.40 80.50 5.10 2001 75.90 81.00 5.10 2002 76.30 81.10 4.80 2003 76.50 81.30 4.80 2004 70.00 81.80 5.00 2005 76.80 81.80 5.00 2008 77.00 82.00 5.00 2007 77.00 82.00 5.00 2008 77.50 8250 5.00 2000 82 80 5.10 2010 77.90 83 00 5.10 2011 78.00 83.60 5.60 2012 78.00 83.40 5.40 2013 78.70 84.00 5.30 2014 78.80 84.10 5.30 2015 78.50 83 70 5.20 2016 78.90 34.00 5.10 2017 78.80 83.90 5.10 2018 79.30 84.40 5.10 5.30 77.70 Mean Sid dev 01 02 03 IQR (15) IOR 73.03 4.08 69.51 74.20 76.55 7.04 10.57 78.38 4.07 74.99 79.30 8145 6.46 9.70 5.34 0.53 5.00 5.18 5.51 051 0.76