Using the dataset "House Prices Data", answer the following questions: 1. Find the mean, median, sample variance, and sample standard deviation for the follow- ing variables: Savings, Income, Educ, Age, and Cons. 2. Create a histogram using the data for Savings. Use the Sturges' rule to calculate how many bins you should include. In your result file, you must include frequency table with bin limits, relative frequencies, and cumulative frequencies, along with your histogram. Discuss the shape of the histogram. What does it tell you about the distribution of annual savings? 3. Calculate skewness of the distribution of Savings. Does it support your interpretation of the shape of the histogram from the previous question? Explain. 4. Do a scatterplot of Savings and Income, where X - Income and Y = Savings. In your result file, include the plot and a discussion of the plot. 5. Do a scatterplot of Savings and Educ, where X = Educ and Y = Savings. In your result file, include the plot and a discussion the plot. 6. Calculate the covariance and correlation coefficient between (1) X = Income and Y = Savings, and (2) X = Educ and Y = Savings. Interpret the two correlation coefficients. I 7. Calculate the confidence intervals for population mean of Savings for 90%, 95%, and 99% confidence levels, assuming that the dataset given is a sample and population standard deviation is unknown. 8. Conduct two-tailed hypothesis tests of f = $1,700 for Savings at 1%, 5%, and 10% sig- nificant levels, assuming that the dataset is a sample and population standard deviation is unknown. 9. The city claims that the population mean for Savings is less than $1,700. Conduct hypothesis tests at 1%, 5%, and 10% significance levels to test that claim, assuming that the dataset is a sample and population standard deviation is unknown. 10. Conduct a two tailed hypothesis tests at 1%, 5%, and 10% significant levels using the confidence interval found in question 7. Do you get the same results as your two tailed hypothesis tests in question 8? Explain. SAVING Sheet1 Educ 2 0 OOOO NON OANA 0 VAN ON 0 0 1 OOO- Cons 1890 11529 6026 5805 6715 5100 22848 13597 11015 8168 9596 11402 6288 10399 5217 4081 4187 2290 7819 olo Savings Income Size 30 1920 874 12403 370 6396 1200 7005 275 6990 1400 6500 3159 26007 1766 15363 3984 14999 1017 9185 1004 10600 687 12089 -34 6254 -1389 9010 1000 6217 1831 5912 613 4800 50 2340 13 7832 1389 9583 602 7600 2221 13858 1588 5802 5082 19362 1846 8000 914 17200 2483 4091 837 9600 1274 10425 -275 6512 1092 7675 1157 12418 340 5079 373 6979 3307 10517 10668 30996 1105 6283 3500 8511 12700 3020 16770 550 5300 5375 2532 6265 6120 8520 Age 2 9 17 9 12 13 17 16 9 16 9 10 11 14 7 8 12 6 12 8 9 17 12 11 10 12 8 10 3 12 12 8 B 12 17 12 12 11 12 16 12 8 12 12 Black 40 33 31 50 28 33 36 44 48 31 41 41 36 31 27 42 28 46 47 35 41 30 38 48 36 45 44 44 46 26 50 46 33 41 33 41 29 27 42 39 36 34 40 37 5 5 5 5 10 4 7 5 5 5 4 2 3 7 3 4 B 3 3 3 6 4 3 4 5 4 5 4 5 4 3 9 5 6 6 4 4 0 0 0 0 1 0 0 0 0 8174 6998 Qool 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 11637 4214 14280 6154 16286 1608 8783 9151 6787 6583 11261 5739 6606 7210 20328 4178 5011 12159 13750 7850 4380 3733 2400 541 0 0 0 0 0 Sheet1 12 17 NABASAN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3733 2400 26975 750 8392 7649 15810 5841 11453 6543 Bese SAVING 2532 6265 6120 8520 -2749 24228 0 750 -1036 7356 1351 9000 -1150 14680 -248 5593 388 11841 1157 7700 1656 10550 3959 13700 5369 12242 1405 7803 220 9879 -298 9154 -276 7087 -578 4496 - 1300 4636 5277 9003 980 13820 2637 8891 984 8832 -76 8385 902 5403 10733 8573 716 5516 200 6000 6 16778 1464 9504 948 8953 835 8703 -2583 12667 298 6504 481 8180 5039 11600 - 111 5602 0 10390 4115 30610 2575 3941 -112 2936 -5577 11068 2750 8338 95 6883 1348 7212 178 10411 -695 6850 787 8354 4542 13923 1260 6214 2687 12323 720 14963 5109 1800 22060 1654 9200 1475 10450 566 25405 12350 4 5 2 5 6 4 5 4 4 3 4 4 G 4 6 2 B 6 4 3 2 6 2 5 2 3 4 3 5 6 3 4 6 6 4 4 4 4 4 7 5 4 3 5 3 2 4 3 4 12 14 15 12 19 14 12 7 12 7 12 11 9 7 10 10 16 & 12 12 10 12 12 12 13 9 16 12 12 9 12 17 9 8 16 9 10 12 14 8 10 10 8 40 37 44 49 33 36 51 37 33 39 44 30 39 46 43 40 40 39 34 32 42 52 29 27 37 52 32 36 31 36 34 54 52 28 44 29 50 80 44 34 39 39 29 38 30 50 33 35 36 33 38 40 50 54 31 27 40 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 9 0 0 0 9741 6573 6398 9659 9452 7343 5074 5996 3728 12840 6254 7648 8461 4501 -2160 5800 5800 16772 8040 8005 7868 15550 6206 7099 6567 5713 10390 26495 1366 3048 16645 5588 658 5864 10233 9545 7547 9281 4954 9636 14243 4951 30260 7576 8075 8572 0 0 0 0 16 12 20 12 4 4 2 10060 8 GB SEELESE 0 0 0 0 0 0 0 0 0 0 0 12 0136 2 5 0 12 SAVING Sheet Variable Saving Income Size Educ Age Black Cons Definition Annual savings, $ Annual income, $ Family size Years of education for household head Age of household head, years = 1 if household head is black Annual consumption, $ Using the dataset "House Prices Data", answer the following questions: 1. Find the mean, median, sample variance, and sample standard deviation for the follow- ing variables: Savings, Income, Educ, Age, and Cons. 2. Create a histogram using the data for Savings. Use the Sturges' rule to calculate how many bins you should include. In your result file, you must include frequency table with bin limits, relative frequencies, and cumulative frequencies, along with your histogram. Discuss the shape of the histogram. What does it tell you about the distribution of annual savings? 3. Calculate skewness of the distribution of Savings. Does it support your interpretation of the shape of the histogram from the previous question? Explain. 4. Do a scatterplot of Savings and Income, where X - Income and Y = Savings. In your result file, include the plot and a discussion of the plot. 5. Do a scatterplot of Savings and Educ, where X = Educ and Y = Savings. In your result file, include the plot and a discussion the plot. 6. Calculate the covariance and correlation coefficient between (1) X = Income and Y = Savings, and (2) X = Educ and Y = Savings. Interpret the two correlation coefficients. I 7. Calculate the confidence intervals for population mean of Savings for 90%, 95%, and 99% confidence levels, assuming that the dataset given is a sample and population standard deviation is unknown. 8. Conduct two-tailed hypothesis tests of f = $1,700 for Savings at 1%, 5%, and 10% sig- nificant levels, assuming that the dataset is a sample and population standard deviation is unknown. 9. The city claims that the population mean for Savings is less than $1,700. Conduct hypothesis tests at 1%, 5%, and 10% significance levels to test that claim, assuming that the dataset is a sample and population standard deviation is unknown. 10. Conduct a two tailed hypothesis tests at 1%, 5%, and 10% significant levels using the confidence interval found in question 7. Do you get the same results as your two tailed hypothesis tests in question 8? Explain. SAVING Sheet1 Educ 2 0 OOOO NON OANA 0 VAN ON 0 0 1 OOO- Cons 1890 11529 6026 5805 6715 5100 22848 13597 11015 8168 9596 11402 6288 10399 5217 4081 4187 2290 7819 olo Savings Income Size 30 1920 874 12403 370 6396 1200 7005 275 6990 1400 6500 3159 26007 1766 15363 3984 14999 1017 9185 1004 10600 687 12089 -34 6254 -1389 9010 1000 6217 1831 5912 613 4800 50 2340 13 7832 1389 9583 602 7600 2221 13858 1588 5802 5082 19362 1846 8000 914 17200 2483 4091 837 9600 1274 10425 -275 6512 1092 7675 1157 12418 340 5079 373 6979 3307 10517 10668 30996 1105 6283 3500 8511 12700 3020 16770 550 5300 5375 2532 6265 6120 8520 Age 2 9 17 9 12 13 17 16 9 16 9 10 11 14 7 8 12 6 12 8 9 17 12 11 10 12 8 10 3 12 12 8 B 12 17 12 12 11 12 16 12 8 12 12 Black 40 33 31 50 28 33 36 44 48 31 41 41 36 31 27 42 28 46 47 35 41 30 38 48 36 45 44 44 46 26 50 46 33 41 33 41 29 27 42 39 36 34 40 37 5 5 5 5 10 4 7 5 5 5 4 2 3 7 3 4 B 3 3 3 6 4 3 4 5 4 5 4 5 4 3 9 5 6 6 4 4 0 0 0 0 1 0 0 0 0 8174 6998 Qool 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 11637 4214 14280 6154 16286 1608 8783 9151 6787 6583 11261 5739 6606 7210 20328 4178 5011 12159 13750 7850 4380 3733 2400 541 0 0 0 0 0 Sheet1 12 17 NABASAN 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3733 2400 26975 750 8392 7649 15810 5841 11453 6543 Bese SAVING 2532 6265 6120 8520 -2749 24228 0 750 -1036 7356 1351 9000 -1150 14680 -248 5593 388 11841 1157 7700 1656 10550 3959 13700 5369 12242 1405 7803 220 9879 -298 9154 -276 7087 -578 4496 - 1300 4636 5277 9003 980 13820 2637 8891 984 8832 -76 8385 902 5403 10733 8573 716 5516 200 6000 6 16778 1464 9504 948 8953 835 8703 -2583 12667 298 6504 481 8180 5039 11600 - 111 5602 0 10390 4115 30610 2575 3941 -112 2936 -5577 11068 2750 8338 95 6883 1348 7212 178 10411 -695 6850 787 8354 4542 13923 1260 6214 2687 12323 720 14963 5109 1800 22060 1654 9200 1475 10450 566 25405 12350 4 5 2 5 6 4 5 4 4 3 4 4 G 4 6 2 B 6 4 3 2 6 2 5 2 3 4 3 5 6 3 4 6 6 4 4 4 4 4 7 5 4 3 5 3 2 4 3 4 12 14 15 12 19 14 12 7 12 7 12 11 9 7 10 10 16 & 12 12 10 12 12 12 13 9 16 12 12 9 12 17 9 8 16 9 10 12 14 8 10 10 8 40 37 44 49 33 36 51 37 33 39 44 30 39 46 43 40 40 39 34 32 42 52 29 27 37 52 32 36 31 36 34 54 52 28 44 29 50 80 44 34 39 39 29 38 30 50 33 35 36 33 38 40 50 54 31 27 40 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 9 0 0 0 9741 6573 6398 9659 9452 7343 5074 5996 3728 12840 6254 7648 8461 4501 -2160 5800 5800 16772 8040 8005 7868 15550 6206 7099 6567 5713 10390 26495 1366 3048 16645 5588 658 5864 10233 9545 7547 9281 4954 9636 14243 4951 30260 7576 8075 8572 0 0 0 0 16 12 20 12 4 4 2 10060 8 GB SEELESE 0 0 0 0 0 0 0 0 0 0 0 12 0136 2 5 0 12 SAVING Sheet Variable Saving Income Size Educ Age Black Cons Definition Annual savings, $ Annual income, $ Family size Years of education for household head Age of household head, years = 1 if household head is black Annual consumption, $