Can someone help me with this thanks.
1. Solve the following problems. Show your COMPLETE solution. 1. An economist claims that the population standard deviation of the monthly income of all the families who belong to the poverty level is Php2,500. A group of researchers surveyed 250 families who belong to the poverty level and obtained a mean monthly income of Php3,500. Assuming that the monthly income of the families is approximately normally distributed, find: a. the point estimate of the population; (1 point) b. the margin of error if the confidence level is 98%; (3 points) and c. the 95% confidence interval of the monthly income of all the families who belong to the poverty level. (7 points) Solution: . Teacher Mitch conducted a periodic examination to all of her students enrolled in Statistics. The scores are normally distributed with a population standard deviation of 10. Teacher Mitch randomly selected 125 students and obtained a mean score of 60. a. What is the population of interest? (1 point) b. What is the point estimate of the population mean? (1 point) c. Compute the standard error of the mean. (2 points) d. At 95% confidence level, what is the margin of error? (3 points) e. Find the 90% confidence interval for the population mean. (7 points) Solution:3. An electrical company manufactures light bulbs for LCD projectors with life spans that are approximately normally distributed. A randomly selected sample of 25 lights bulbs have a mean life span of 600 hours with a standard deviation of 50 hours. a. Compute the margin of error at 95% confidence level. (3 points) b. What is the value of the point estimate? (1 point) c. Find the 98% confidence interval for the population mean of all the light bulbs produced by the electrical company. (7 points) Solution: 4. A randomly selected 20 packs of brand X laundry soap manufactured by a well-known company have contents that are 120g, 122g, 119g, 112g, 123g, 121g, 118g, 115g, 125g, 109g, 108g, 127g, 110g, 120g, and 117g. a. Compute the margin of error at 90% confidence level. (3 points) b. Compute the value of the point estimate. (2 points) c. Find the 95% confidence interval for the mean assuming that the population of the laundry soap content is approximately normally distributed. (7 points) Solution:5. Based on the results of a survey conducted by a group of researchers, the proportion of females holding executive positions in the government agencies in a certain populated city in the Philippines I normally distributed. In a random sample of 300 female employees in government agencies, 75 female employees hold executive positions. a. Compute the proportion estimate of the parameter. (2 points) b. Compute the margin of error of the proportion at 90% confidence level. (3 points) c. Find the 95% and 98% confidence interval for all the female employees in the government agencies holding executive positions. (12 points) Solution:t - Distribution Table cum. tso $ 75 t.80 t 85 too prob. t95 $975 t.99 t995 t 999 t.9995 one - 0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 tail two - 1.00 0.50 tails 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001 df 1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.31 636.62 2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599 3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 10.215 12.924 4 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.000 0.706 0.889 1.108 1.397 .860 2.306 2.896 3.355 4.501 5.041 9 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.92 3.686 4.015 17 0.000 0.689 0.863 1.069 1.333 1.740 2.1 10 2.567 2.898 3.646 3.965 18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.000 0.687 0.860 1.064 1.325 .725 2.086 2.528 2.845 3.552 3.850 21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 0.000 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768 24 0.000 0.685 0.857 1.059 1.308 1.711 2.064 2.492 2.797 3.467 3.745 25 0.000 .684 0.856 1.058 1.316 1,708 2.060 2.485 2.787 3.450 3.725 26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 0.000 0.684 0.855 .05 1.314 1.703 2.052 2.473 2.771 3.421 3.690 28 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.000 0.683 0.854 1.055 1.311 1.695 2.045 2.462 2.756 3.396 3.659 30 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 40 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460 80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639 3.195 3.416 100 0.000 0.677 0.845 1.042 1.290 1.660 1.984 2.364 2.626 3.174 3.390 1000 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581 3.098 3.300 0.000 0.674 0.842 1.036 1.282 1.645 1.962 2.326 2.576 3.090 3.291 0% 50% 60% 70% 80% 90% 95%% 98% 99% 99.8% 99.9% Confider
