Question

In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $913.

Answer 1

2 n=22 We have: o = $650 S=$913 and a=0.01 The Null and alternative hypothesis Hoo o= 650 o 650 Hi : The test statistic is (n-1)5² 21x9132 41.4318 650² The degree of freedom on 2² ů 21. Critical value: 2 0.01 = 38.93 (one-tailed) Since, the observed value of the teste statistic is greater than the critical value. reject Ho. Hence, we support the claim for men without college degrees in that town , incomes have a higher standard deviation.

alternative hypothesis (ny) s2 0-2 3.5² We have a o= 3.5 n = 17 9 s=4.7 Q = 0.10 The Null and Ho : o=3.5 Hii o +3.5 The test statistic is 2² 16 x 4.7² 28.8522 The degrees of freedom X² is 16. Cautical value: 246,0.05 = 26.30 (two-tailed) Since, The observed value of the test statistic is greater than the critical value. So, we reject Ho. Hence, we support the claim that the new production method has lengthe with a standard deviation different from 35 cm. on

Percentage Points for the x-distribution 1% 0.5% 0.1% 0.05% 2.5% 5% 10% 20% P= 50% 40% 30% V 1 12.12 15.20 17.73 20.00 10.83 13.82 16.27 18.47 0.4549 0.7083 1.074 1.642 2.706 3.841 5.024 6.635 7.879 1.386 1.833 2.408 3.219 4.605 5.991 7.378 9.210 10.60 2.366 2.946 3.665 4.642 6.251 7.815 9.348 11.34 12.84 3.357 4.045 4.878 5.989 7.779 9.488 11.14 13.28 14.86 2 3 4 5 6 7 8 9 4.351 5.132 6.064 7.289 9.236 11.07 5.348 6.211 7.231 8.558 10.64" 12.59 6.346 7.283 8.383 9.803 12.02 14.07 7.344 8.351 9.524 11.03 13.36 15.51 8.343 9.414 10.66 12.24 14.68 16.92 12.83 15.09 16.75 14.45 16.81 18.55 16.01 18.48 20.28 17.53 20.09 21.95 19.02 21.67 23.59 20.51 22.46 24.32 26.12 27.88 22.11 24.10 26.02 27.87 29.67 10 11 12 13 14 9.342 10.34 11.34 12.34 13.34 10.47 11.78 13.44 15.99 11.53 12.90 14.63 17.28 12.58 14.01 15.81 18.55 13.64 15.12 16.98 19.81 14.69 16.22 18.15 21.06 18.31 19.68 21.03 22.36 23.68 20.48 21.92 23.34 24.74 26.12 23.21 24.73 26.22 27.69 29.14 25.19 26.76 28.30 29.82 31.32 29.59 31.26 32.91 34.53 36.12 31.42 33.14 34.82 36.48 38.11 15 16 17 18 19 14.34 15.34 16.34 17.34 18.34 15.73 17.32 16.78 18.42 17.82 19.51 18.87 20.60 19.91 21.69 19.31 20.47 21.61 22.76 23.90 22.31 25.00 23.54 26.30 24.77 27.59 25.99 28.87 27.20 30.14 27.49 28.85 30.19 31.53 32.85 30.58 32.80 32.00 34.27 33.41 35.72 34.81 37.16 36.1938.58 37.70 39.25 40.79 42.31 43.82 39.72 41.31 42.88 44.43 45.97 20 21 22 23 24 19.34 20.34 21.34 22.34 23.34 20.95 22.77 21.99 23.86 23.03 24.94 24.07 26.02 25.11 27.10 25.04 28.41 26.17 29.62 27.30 30.81 28.43 32.01 29.55 33.20 31.41 32.67 33.92 35.17 36.42 34.17 37.57 35.48 38.93 36.78 40.29 38.08 41.64 39.36 42.98 40.00 41.40 42.80 44.18 45.56 45.31 46.80 48.27 49.73 51.18 47.50 49.01 50.51 52.00 53.48 25 26 27 28 29 24.34 25.34 26.34 27.34 28.34 26.14 28.17 27.18 29.25 28.21 30.32 29.25 31.39 30.28 32.46 30.68 31.79 32.91 34.03 35.14 34.38 35.56 36.74 37.92 39.09 37.65 38.89 40.11 41.34 42.56 40.65 41.92 43.19 44.46 45.72 44.31 45.64 46.96 48.28 49.59 46.93 48.29 49.65 50.99 52.34 52.62 54.05 55.48 56.89 58.30 54.95 56.41 57.86 59.30 60.73 30 32 34 36 38 29.34 31.32 31.34 33.38 33.34 35.44 35.34 37.50 37.34 39.56 33.53 35.66 37.80 39.92 42.05 36.25 38.47 40.68 42.88 45.08 40.26 42.58 44.90 47.21 49.51 43.77 46.19 48.60 51.00 53.38 46.98 49.48 51.97 54.44 56.90 50.89 53.67 53.49 56.33 56.06 58.96 58.62 61.58 61.16 64.18 59.70 62.49 65.25 67.98 70.70 62.16 64.99 67.80 70.59 73.35 40 50 60 70 80 39.34 49.33 59.33 69.33 79.33 41.62 51.89 62.13 72.36 82.57 44.16 54.72 65.23 75.69 86.12 47.27 58.16 68.97 79.71 90.41 51.81 63.17 74.40 85.53 96.58 55.76 59.34 63.69 66.77 67.50 71.42 76.15 79.49 79.08 83.30 88.38 91.95 90.53 95.02 100.4 104.2 101.9 106.6 112.3 116.3 73.40 86.66 99.61 112.3 124.8 76.10 89.56 102.7 115.6 128.3 101.1 111.7 92.76 96.52 102.9 113.1 124.3 107.6 118.5 89.33 99.33 128.3 140.2 118.1 124.1 129.6 135.8 90 100 137.2 149.4 140.8 153.2 106.9