Question

(Exercise 8.21 (Algorithmic)} Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States, and Europe (The Wall Street Journal February 15, 2006). Data (annual consumption in liters) consistent with the findings reported in The Wall Street Journal article are shown for a sample of 20 European young women. 51 82 199 174 97 170 164 222 94 115 122 129 169 1710 93 0 93 110 505 Assuming the population is roughly symmetric, calculate the sample mean and sample standard deviation. Then construct a 95% confidence interval for the mean annual consumption of alcoholic beverages by European young women (Round all answers to 1 decimal). The mean is 138 and the standard deviation is 104.8 ♡ The confidence intervall ( 01 180

Answer 1

Here sample size is < 30 so we will use t-ditribution to find 95% confidence interval

The provided sample mean is X = 138 and the sample standard deviation is s = 104.8. The size of the sample is n = 20 and the required confidence level is 95%. The number of degrees of freedom are df = 20 -1 = 19, and the significance level is a = 0.05. Based on the provided information, the critical t-value for a = 0.05 and df = 19 degrees of freedom is te = 2.093. The 95% confidence for the population mean u is computed using the following expression CI= (stom 8+ tomon) Therefore, based on the information provided, the 95% confidence for the population mean u is . 2.093 x 104.8 190 2.093 x 104.8 CI = 138 - 20 20 ) = (138 - 49.048,138 + 49.048)

so the 95% confidence interval is ((89,187)

use following t-table for finding t-critical that is tc

t Table cum. probl one-tail two-tails t so - 0.50 1.00 t 0.25 0.50 t.3o 0.20 0.40 t 35 0.15 0.30 t.90 0.10 0.20 t 95 0.05 0.10 .975 0.025 0.05 t 99 0.01 0.02 995 0.005 0.01 999 0.001 0.002 9995 0.0005 0.001 OOOOOWN 2 318.31 22.327 10.215 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 636.62 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 .848 0.846 1.963 1.386 1.250 1.1901 1.156 1.134 1.119 1.108 1.100 1 .093 1.088 1.083 1 1.079 1 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.045 1.043 3.078 6.314 1.886 2.920 1.638 2 .353 .5332.132 1.476 2.015 1.440 1.943 1.415 1.895 1.397 1.860 1.383 1.833 1.372 1.812 1.363 1.796 .356 1.782 .350 1.771 1.345 1.761 1.341 1.753 1.337 1.746 1.333 1.740 1.330 1.734 1.328 1.729 1.325 1.725 1.323 1.721 1.321 1.717 1.319 1.714 .318 1.711 1.316 1.708 1.315 1.706 1.314 1.703 1.313 1.701 1.311 1.699 1.310 1.697 1.303 1.684 1.296 1.671 1.292 1.664 12.71 31.82 4.303 6.965 3.182 4.541 2.776 3.747 2.571 .447 3.143 2.365 2.998 2.306 2.896 2.262 2.821 2.228 2.764 2.2012 .718 2.1792.681 2.160 2.650 2.145 2.624 2.131 2.602 2.120 2.583 2.110 2.567 2.101 2.552 2.093 2.539 2.086 2.528 2.080 2.518 2.074 2.508 2.069 2.500 2.064 2.492 2.060 2.485 2.056 2.479 2.052 2.473 2.048 2.467 2.045 2.462 2.042 2.457 2.021 2.423 2.000 2.390 1.990 2.374 63.66 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.639 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.195 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416 0