Problem 1 A chief executive officer (CEO) of an IT company claims that the employees in his company, all have above average intelligence. A random sample of thirty employees IQ scores have a mean score of 112. The mean population IQ is 100 with a standard deviation of 15. IQ scores are normally distributed. Use a level of significance ?=5%.A. Describe the null and alternate hypothesis.B. Infer whether there is sufficient evidence to support the CEO's claim, throughappropriate step by step procedure?Refer to z-table (Table 1) attached hereProblem 2 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find 96% confidence interval for the population mean of all bulbs produced by this firm. Infer, as to how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10hours of the true mean?

All Questions refer to CLO3/C4/P4 Problem 1 (5) A chief executive officer (CEO) of an IT company claims that the employees in his company, all have above average intelligence. A random sample of thirty employees IQ scores have a mean le 1 score of 112. The mean population IQ is 100 with a standard deviation of 15. IQ scores are normally distributed. Use a level of significance a =5%. D(2) |2 (2) |z 1(2)|z 0(2)|z (2) | 2 (2) I A. Describe the null and alternate hypothesis. 0.00 0.5000 | 0.50 0.6915 | 1.00 0.8413 1.50 0.9332 |2.00 0.97725 |2.50 0.99379 0.01 0.5040 0.51 0.6950 1.01 0.8438 1.51 0.9345 2.01 0.97778 2.51 0.99396 B. Infer whether there is sufficient evidence to support the CEO's claim, through 0.02 0.5080 0.52 0.6985 1.02 0.8461 1.52 0.9357 2.02 0.97831 2.52 0.99413 0.03 0.5120 0.53 0.7019 1.03 0.8485 1.53 0.9370 2.03 0.97882 2.53 0.99430 appropriate step by step procedure? 0.04 0.5160 0.7054 1.04 0.8508 1.54 0.9382 12.04 0.97932 2.54 0.99446 0.05 0.5199 0.55 0.7088 1.05 0.8531 1.55 0.9394 2.05 0.97982 2.55 0.99461 Refer to z-table (Table 1) attached here 0.06 0.5239 0.56 0.7123 1.06 0.8554 1.56 0.9406 2.06 0.98030 2.56 0.99477 0.07 0.5279 0.57 0.7157 1.07 0.8577 1.57 0.9418 2.07 0.98077 2.57 0.99492 0.08 0.5319 0.58 0.7190 1.08 0.8599 158 0.9429 2.08 0.98124 2.58 0.99506 0.09 0.5359 0.59 0.7224 0.8621 1.59 0.9441 2.09 0.98169 2.59 0.99520 0.10 0.5398 0.60 0.7257 1.10 0.8643 1.60 09452 2.10 0.98214 2.60 0.99534 0.11 0.5438 0.61 0.7291 0.8665 61 0.9463 0.98257 0.99547 0.12 0.5478 0.62 0.7324 0.8686 1.62 0.9474 2.12 0.98300 2.62 0.99560 0.13 0.5517 0.63 0.7357 1.13 0.8708 1.63 0.9484 2.13 0.98341 2.63 0.99573 0.14 0.5557 0.7389 0.8729 1.64 0.9495 0.98382 0.99585 0.15 5 0.5596 0.65 0.7422 1.15 0.8749 1 65 0.9505 2.15 0.98422 2.65 0.99598 0.16 0.5636 0.66 0.7454 1.16 0.8770 165 0.9515 2.16 0.98461 2.66 0.99609 0.17 0.5675 0.67 0.7486 1.17 0.8790 1.67 0.9525 2.17 0.98500 2.67 0.99621 0.18 0.5714 0.68 0.7517 1.18 0.8810 1.68 0.9535 2.18 0.98537 2.68 0.99632 0.19 0.5753 0.69 0.7549 0.8830 0 0545 2.19 0.98574 2.69 0.99643 0.20 0.5793 0.70 0.7580 1.20 0.8849 1.70 0.9554 2.20 0.98610 2.70 0.99653 0.21 0.5832 0.71 0.7611 0.8869 0.9564 0.98645 0.99664 0.22 0.5871 0.72 0.8888 172 0.9573 0.98679 0.99674 0.23 0.5910 0.73 0.7673 0.8907 1.73 0.9582 2.23 0.98713 0.99683 0.24 0.5948 0.74 0.7704 0.8925 0.9591 0.98745 0.99693 0.25 0.5987 0.75 0.7734 0.8944 1.75 0.9599 0.98778 0.99702 0.26 0.6026 0.76 0.7764 0.8962 0.960 0.98809 0.99711 0.27 0.6064 0.77 0.7794 0.8980 1.77 0.9616 2.27 0.98840 0.99720 0.28 0.6103 0.78 0.7823 0.8997 0.9625 2.28 0.98870 2.78 0.99728 0.29 0.6141 0.79 0.7852 0.9015 1.79 0 9633 2.29 0.98899 0.99736 0.30 0.6179 0.80 0.7881 1.30 0.9032 1 90 0.9641 2.30 0.98928 2.80 0.99744 0.31 0.6217 0.81 0.7910 0.9049 1.81 0.964 0.98956 0.99752 0.32 0.6255 0.82 0.7939 1.32 0.9066 18 0.9656 2.32 0.98983 2.82 0.99760 0.33 0.6293 0.83 0.7967 0.9082 1.83 0.9664 2.33 0.99010 2.83 0.99767 0.34 0.6331 0.84 0.7995 0.9099 0.9671 0.99036 0.99774 0.35 0.6368 0.85 0.8023 0.9115 0.9678 2.35 0.99061 2.85 0.99781 Problem 2 (5) 0.36 0.6406 0.86 0.8051 0.9131 0.9686 0.99086 0.99783 0.37 0.6443 0.87 0.8078 1.37 0.9147 0.0693 2.37 0.99111 0.99795 0.38 0.6480 0.88 0.8106 1.38 0.9162 0.9699 2.38 0.99134 0.99801 An electrical firm manufactures light bulbs that have a length of life that is approximately 0.39 0.6517 0.89 0.8133 0.9177 1.89 0.9706 2.39 0.99158 0.99807 0.40 0.6554 0.90 0.8159 1.40 0.9192 1.90 0.9713 2.40 0.99180 2.90 0.99813 normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an 0.41 0.6591 0.91 0.8186 0.9207 191 0.9719 0.99202 0.99819 0.42 0.6628 0.92 0.8212 1.42 0.9222 1.92 0.9726 0.99224 2.92 0.99825 average life of 780 hours, find 96% confidence interval for the population mean of all bulbs 0.43 0.6664 0.93 0.8238 0.9236 1.93 0.9732 2.43 0.99245 0.99831 0.44 0.6700 0.94 0.8264 0.9251 194 0.9738 2.44 0.99266 0.99836 produced by this firm. Infer, as to how large a sample is needed if we wish to be 96% confident 0.45 0.6736 0.95 0.8289 0.9265 1.95 0.9744 2.45 0.99286 2.95 0.99841 0.46 0.6772 0.96 0.8315 0.9279 1.96 0.9750 0.99305 0.99846 that our sample mean will be within 10hours of the true mean? 0.47 0.6808 0.97 0.8340 0.9292 1.97 0.9756 2.47 0.99324 2.97 0.99851 0.48 0.6844 0.98 0.8365 0.9306 0.9761 0.99343 0.99856 0.49 0.6879 0.99 1 49 0.9319 0.9767 0.99361 0.99861