Exercise 7-22 Algo

Consider a population proportion p = 0.29. [You may find it useful to reference the z table.]

a. What is the expected value and the standard error of the sampling distribution of the sample proportion with n = 11 and n = 67? (Round the standard error to 4 decimal places.)

b. Can you conclude that the sampling distribution of the sample proportion is normally distributed for both sample sizes?

multiple choice 1

• Yes, the sampling distribution of the sample proportion is normally distributed for both sample sizes.
• No, the sampling distribution of the sample proportion is not normally distributed for either sample size.
• No, only the sample proportion with n = 11 will have a normal distribution.
• No, only the sample proportion with n = 67 will have a normal distribution.

c. If the sampling distribution of the sample proportion is normally distributed with n = 11, then calculate the probability that the sample proportion is between 0.27 and 0.29. (If appropriate, round final answer to 4 decimal places.)

multiple choice 2

• We cannot assume that the sampling distribution of the sample proportion is normally distributed.
• We can assume that the sampling distribution of the sample proportion is normally distributed and the probability that the sample proportion is less than 12.5 is

d. If the sampling distribution of the sample proportion is normally distributed with n = 67, then calculate the probability that the sample proportion is between 0.27 and 0.29. (If appropriate, round final answer to 4 decimal places.)

multiple choice 3

• We cannot assume that the sampling distribution of the sample proportion is normally distributed.
• We can assume that the sampling distribution of the sample proportion is normally distributed and the probability that the sample proportion is less than 12.5 is

TABLE 1 Standard Normal Curve Areas Entries in this table provide cumulative probabilities, that is, the area P (ZS - 2) under the curve to the left of -z. For example, P(Z S -1.52) = 0.0643. -Z 0 Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0000 0.0000 0.0000 0.0000 -3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 -3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.7 0.0001 0.0001 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 -3.6 -3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3. 0.0005 0.0004 0.0004 0.0004 0.0003 -3.3 0.0005 0.0005 0.0004 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 0.0012 0.0010 0.0013 0.0013 0.0011 0.0011 0.0010 -3.0 0.0013 0.0012 0.0011 0.0014 0.0014 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0038 0.0037 0.0036 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0049 0.0048 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0069 0.0068 0.0066 0.0064 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3 0.0107 0.0104 0.0136 0.0132 0.0129 0.0125 0.0122 0.01 19 0.0116 0.0113 0.01 10 -2.2 0.0139 0.0143 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1. 0.0322 0.0301 0.0294 0.0359 0.0351 0.0344 0.0336 0.0329 0.0314 0.0307 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 0.0446 0.0436 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 0.0571 0.0559 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0681 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 0.0968 0.0951 0.1131 0. 1093 0.1003 0.0985 0.1151 0.1112 0.1075 0.1056 0.1038 0.1020 0.1170 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1401 0.1379 10 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2389 0.2358 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2420 0.2327 0.2451 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.3594 0.3557 0.3520 0.3483 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.4207 0.4052 0.3936 0.3859 -0.2 0.4168 0.4129 0.4090 0.4013 0.3974 0.3897 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.5398 0.6026 0.6064 0.6103 0.6141 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.6879 0.4 0.6591 0.6700 0.6736 0.6844 0.6554 0.6628 0.6664 0.6772 0.6808 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5 0.6915 0.6950 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.8485 0.8508 0.8554 0.8599 0.8621 1.0 0.8413 0.8438 0.8461 0.8531 0.8577 0.8810 0.8830 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.9015 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9332 0.9345 0.9495 0.9505 0.9535 0.9545 0.9452 0.9463 0.9474 0.9484 0.9515 0.9525 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 20 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9772 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4 0.9918 0.9920 0.9952 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9974 0.9975 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.9990 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9995 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9996 0.9997 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 0.9998 0.9998 0.9998 3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.6 0.9998 0.9998 3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 3.8 1.0000 39 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Source: Probabilities calculated with Excel