The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 45 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $30, and the standard deviation for female consumers is assumed to be $18. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)? 67.03 b. At 99% confidence, what is the margin of error (to 2 decimals? c Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use 2-table, TABLE 1 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION (Continued) Cumulative probability Entries in the table give the area under the curve to the left of the z value. For example, for 2 -1.25, the cumulative probability is 8944 0 z 2 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0 .1 2 .3 4 S000 5398 5793 .6179 .6554 5040 5438 5832 .6217 .6591 5080 5478 5871 .6255 .6628 5120 5517 5910 .6293 .6664 5160 5557 5948 .6331 6700 .5199 .5596 .5987 .6368 6736 5239 5636 6026 .6406 6772 5279 5675 6064 .6443 .6808 5319 5714 .6103 6480 6844 5359 5753 6141 6517 6879 5 .6 .7 .8 .9 .6915 .7257 .7580 .7881 .8159 -6950 .7291 .7611 .7910 .8186 6985 .7324 7642 .7939 .8212 .7019 .7357 .7673 .7967 8238 .7054 .7389 .7704 .7995 8264 .7088 .7422 .7734 8023 .8289 .7123 .7454 .7764 8051 8315 7157 7486 .7794 .8078 8340 17190 .7517 .7823 8106 -8365 .7224 .7549 .7852 8133 8389 1.0 1,1 1.2 1.3 1.4 8413 8643 8849 .9032 .9192 .8438 .8665 8869 .9049 9207 .8461 .8686 .8888 .9066 .9222 .8485 .8708 .8907 .9082 9236 .8508 8729 .8925 9099 9251 .8531 .8749 .8944 9115 9265 .8554 .8770 .8962 9131 9279 .8577 8790 .8980 9147 8599 8810 .8997 9162 9306 8621 8830 9015 9177 9319 9292 1.5 1.6 1.7 1.8 1.9 .9332 9452 9554 9641 9713 9345 9463 9564 9649 .9719 9357 9474 .9573 .9656 .9726 9370 9484 .9582 9664 9732 .9382 .9495 .9591 9671 .9738 9394 .9505 9599 .9678 .9744 .9406 9515 9608 9686 9750 9418 9525 9616 9693 9756 9429 9535 9625 9699 9761 9441 9545 9633 9706 9767 2.0 2.1 2.2 2.3 24 9772 9821 9861 .9893 9918 .9778 9826 9864 9896 9920 .9783 .9830 .9868 .9898 .9922 9788 .9834 9871 9901 9925 .9793 .9838 9875 .9904 9927 9798 .9842 .9878 9906 .9929 9803 9846 9881 9909 9931 9808 9850 .9884 .9911 9932 9812 9854 .9887 9913 9934 .9817 9857 9890 9916 9936 25 2.6 2.7 2.8 2.9 9938 .9953 9965 9974 9981 9940 .9955 9966 9975 9982 .9941 .9956 9967 9976 9982 9943 9987 9968 .9945 .9959 .9969 9977 9984 9946 9960 .9970 .9978 9984 9948 9961 9971 .9979 9985 9949 9962 .9972 9979 9985 9951 9963 9973 9980 9986 9952 9964 .9974 9981 9986 .9977 .9983 3.0 9987 9987 9987 .9988 9988 .9989 9989 9989 9990 9990
