3. As part of an environmental Studies class project, students measured the circumference of a sample of 45 Blue Spruce Trees near the lake. The sample mean of circumference was 29.8 inches Assume the population standard is known to be 7.2 inches. Find a 90% confidence interval for the population mean circumference of all Blue Spruce trees near the lake (USE z distribution)Areas of a Standard Normal Distribution continued Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 -5000 .5040 .5080 .5120 5160 .5199 5239 .5279 5319 .5359 0.1 5398 .5438 .5478 .5517 5557 .5596 .5636 .5675 5714 .5753 0.2 .5793 .5832 .5871 5910 .5948 .5987 6026 6064 6103 6141 0.3 .6179 .6217 .6255 6293 6331 .6368 .6406 .6443 .6480 .6517 0.4 6554 .6591 6628 6664 6700 .6736 6772 6808 .6844 .6879 0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224 Table entry for z is the area 0.6 .7257 .7291 .7324 .7357 .7389 .7422 7454 .7486 .7517 .7549 to the left of z. 0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133 0.9 .8159 .8186 8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 1.0 .8413 8438 8461 8485 .8508 .8531 8554 8577 .8599 .8621 1.1 .8643 .8665 .8686 -8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .BB49 -8869 .8888 .8907 .8925 .8944 .8962 8980 .8997 9015 1.3 .9032 9049 -9066 9082 .9099 9115 .9131 .9147 9162 9177 1.4 .9192 .9207 .9222 9236 9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 9357 .9370 .9382 .9394 .9406 9418 .9429 9441 1.6 .9452 .9463 .9474 9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 -9564 .9573 .9582 .9591 .9599 9608 .9616 .9625 .9633 1.8 9641 .9649 .9656 9664 9671 .9678 .9686 9693 .9699 .9706 1.9 9713 .9719 .9726 .9732 .9738 9744 9750 .9756 .9761 .9767 2.0 .9772 9778 .9783 .9788 .9793 9798 .9803 .9808 9812 9817 2.1 .9821 .9826 9830 9834 .9838 .9842 .9846 .9850 .9854 .9857 2.2 9861 .9864 .9868 .9871 .9875 .9878 9881 9884 .9887 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 9913 9916 2.4 .9918 .9920 .9922 -9925 .9927 .9929 9931 .9932 .9934 9936 2.5 9938 9940 .9941 .9943 .9945 .9946 .9948 9949 .9951 .9952 2.6 9953 -9955 .9956 .9957 .9959 9960 .9961 .9962 .9963 .9964 2.7 9965 .9966 -9967 9968 .9969 .9970 9971 .9972 9973 .9974 2.8 .9974 .9975 .9976 .9977 .9977 .9978 9979 .9979 .9980 9981 29 9981 9982 .9982 9983 .9984 .9984 .9985 .9985 .9986 .9986 Areas of a Standard 3.0 9987 .9987 .9987 9988 .9988 .9989 9989 9989 .9990 .9990 Normal Distribution continued 3.1 9990 .9991 .9991 .9991 .9992 .9992 9992 9992 .9993 .9993 (b) Confidence Interval 3.2 9993 .9993 .9994 9994 9994 .9994 .9994 9995 .9995 .9995 Critical Values Z 3.3 9995 .9995 .9995 .9996 .9996 .9996 .9996 9996 .9996 9997 Critical 9997 .9997 9997 9997 9997 .9997 .9997 .9997 .9997 .9998 Level of Confidence c Value Zz For 2 values greater than 3.49, use 1.000 to approximate the area. 0.70, or 70%% 1.04 Areas of a Standard Normal Distribution continued 0.75, or 750% 1.15 0.80, or 80% 1.28 (c) Hypothesis Testing, Critical Values zo 0.85, or 85% 1.44 Level of Significance 4 = 0.05 4 = 0.01 0.90, or 90% 1.645 0.95, or 95% 1.96 Critical value Zo for a left-tailed test -1.645 -2.33 0.98, or 98% 2.33 Critical value Zo for a right-tailed test 1.645 2.33 0.99, or 99% 2.58 Critical values +Zo for a two-tailed test $1.96 +2.58
