Question

Using the sample of size 200, construct a 95% confidence interval for the proportion of Youth Survey participants who would describe themselves as being about the right weight (Round to three decimal places.) Sample Proportion = Margin of error Lower limit Upper limit Does your 95% confidence interval based on the sample of size 200 include the true proportion of Youth Survey participants who would describe themselves as being about the right weight? O Yes O No

Answer 1

Since the sample proportion is not given then it is assumed that the sample proportion is 0.50. Now.

# Sample proportion=0.50

# Margin of error,E is calculated as

p(1-P) Vn

10.50(1 -0.50) = 1.96 * 1 200

= 0.069

# The Confidence Interval is calculated as

PIE

0.50 +0.069

={0.431, 0.569}

The Z score is computed using the Z table shown below:

# Can't say without the true population that says the right weight.

#Z table

Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores -3.4 -3.3 7 00 0.1 0.2 -3.2 03 -3.0 05 -2.8 -2.7 0.6 0.7 0.8 0.9 25 -2.4 1.0 1.1 -22 1.5 -1.9 -1.8 0.00 0.0003 0.0005 0.0002 0.0010 0.0013 0.0019 0.0026 0.0035 0.0047 0.0062 0.0082 0.0107 0.0139 0.0179 0.0078 0.0287 0.0399 0.1446 0.0548 | 0.0668 0.008 0.0968 0.1151 0.1357 0.1587 0.1841 0.2119 0.2420 0.2743 0.3085 0.34.16 0.3821 0.4207 0.4602 0.50m) 001 .02 0.03 0.04 0.05 0.06 0.07 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0005 0.0005 0.0004 0.0004 (JCKX14 OCX4 OUXX14 0.0002 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0009 0.0009 0.0009 0.0CON O CKXIA OCCIS DIKI8 D.DOI3 0.0013 0.0012 0.0012 0.0011 0110 0011 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0025 0.0024 0.0023 0.0023 0.0022 OLC021 0.002 0.0034 0.0033 0.0032 0.0031 0.0000 0029 0.0028 0.0015 0.0014 0.0013 0.001 0.0010 0.0039 0.0038 D.DCX0 0.00590 .0057 0.0055 0.0054 0.0052 0.005 0.0080 0.0078 0.0075 0.0023 0.0071 0.0069 0.0068 DDI04 0.0102 (0 ) .0004 0.000 0.00 0.0136 0.0132 0.0129 0.0125 0.0122 0 0119 0.0116 0.0174 0.0170 0.0166 0.0162 0.0158 00154 0.015O 0.0072 0.0217 0.02120 0207 0.0202 00197 0.0192 0.0281 0.0274 0.0268 0.0262 0.0256 002SD 0.0244 0.035 0.034400016 0.0000012200114 0.0207 0.0476 0.0427 0.0418 0.04000.0401 040192 0.0194 0.0537 0.0S26 0.0S16 0.OSOS 0.0495 04185 0.0475 01655 0.0643 0,06% 0,06180,0606 00594 0.0592 0.793 0.0278 0.0764 0.0749 0.0735 0721 0.0708 0.0951 0.0934 0.0918 0.0901 0.0885 00869 0 0853 0,1131 0 1112 (1093 0.1075 0.1056 0.1038 0.1020 0.1335 0.1314 0,1292 0 ,1271 0.125 0.12.30 0.1210 0.1562 0.1549 01515 0.1492 0.1469 0.1446 0.1423 013140 .1788 0.1762 0.1736 0.17110 .1635 0.1660 0.20%) 0.2361 0.2033 0.2005 0.1977 0.1949 0.1922 0.2389 0 .2358 0.2227 0.2296 0,2266 02236 0.2206 0.2709 0.2676 0.2643 0.2611 0.2578 02946 0.2514 0.3050 0.3015 0.2981 0.2916 0.2912 0.2877 0.2843 0.3409 0.3372 0.3336 0.3300 0 3264 0.3228 0.3192 .3783 0.3745 0.3707 0.3669 0.3632 3594 0.3557 0.4168 0.4129 0 .1000) 0.4052 0.4013 0.3974 0.3936 0.4562 0.4522 .4483 0.4443 0.4404 0.4364 04325 0.496 0.4920 0,4880 0 4940 0.4801 0.4761 0.4721 0.08 0.00 0.0003 0.0002 0.0024 0.0003 0.0005 0.0005 0.0007 0.0007 0.0010 0.0010 0.0014 0.0014 0.0020 D.0019 0.0027 0.0026 0.0037 0.0036 0.0049 0.0048 0.0066 0.0064 0.0087 D.0084 0.0113 0.0110 0.0146 0.0143 0.0188 D.0183 0.0239 0.0233 0. 001 0.0204 0.0375 0.0367 0.0465 0.0435 0.0571 D.0559 0.0694 0.0681 0.0838 0.0823 0.1003 D 0085 0.1190 0.1170 014010.1379 0.1635 0.161! 0.1994 D.1367 0.2177 0.2148 0.2483 0.2451 0.2810 0.2776 0.3156 0.3121 0.3520 0.483 0.2897 0.3859 0.4286 0.4247 0.4681 0.4641 000 001 D 02 0.03 0.04 0.05 0.06 0.07 0.08 0.00 0 5000 0.5040 0,5080 0.512005160 05199 05239 D.5279 0.531905359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0 25636 D 5675 0.5714 0.5753 0.5793 0.5832 0.58710.5910 059.18 0.5987 0.6026 0.6061 0610306141 0.6179 0.6217 0.6255 0.6293 06331 0.6 668 0.6406 0.6443 0.6480 0.6517 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6T72 0.6806 0.6844 0.6879 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.750 0.7611 0.7642 0.7673 07704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.816 0.8212 0.82330.3264 0.329 0.3315 D.5240 0.8365 0.8359 0.8413 0.8438 0.8461 0.8485 0.85080.8531 0.8554 0.8577 0.8599 0.8621 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8890 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 0.9032 0.9019 0.9066 0.9082 09099 0.9115 0.91310.9147 0.9162 0.9177 0.002 0.9207 0.0222 0.9236 09251 09265 09279 0.92020.9306 0.9319 0.9332 0.9345 0.9357 0.9320 09382 0.9394 0.9406 0.9418 0.9429 0.9441 0.0452 0.0463 0.0474 0.0484 00495 D9505 09515 0.0525 09535 0.0545 0.0554 0.0564 0.0973 09582 00591 09990 DOO D .7616 0.9625 0.9633 0.9641 0.9649 0.9656 0.9664 096210.9678 0.9686 0.9693 0.9699 0.9206 0.9713 0.9719 0,9726 0,9732 0,0738 0.9744 09750 9756 0.9761 09767 0.9772 0.9778 0.9783 0.9288 0.9793 0.9798 099030.9806 0.98120.9817 0.98210 .9826 0.0830 0.9834 09838 0.98420 .9846 0.9850 0.9854 0.9857 0.9861 09864 0.9868 0.0871 09875 0.9878 0.988 D 9884 09887 0.9800 0.9893 0.9296 0.9898 0.9901 0 9904 0.9906 0.99x09 0.99110.9913 0.9916 0.9918 0.99200,9922 0.9925 00927 0.9929 0 9931 0.9032 0.9934 0.9936 0.9938 0.9940) 0.0941 0.943 099450.9946 0.9948 0.9949 0.99s1 0.0952 0.9953 0.995S 0.9956 0.9997 0.9959 0.9960 0.99610.9962 9 963 0.9964 09965 0.9966 0.9967 0.9268 00069 0.9970 09971 0.9072 09973 0.9974 0.9974 0.0075 0,0076 0,977 0.9977 0.9978 0.9981 0.9982 0.9982 0.9983 09984 0.9984 0.9985 0.9985 0.9986 0.9986 09987 0.9987 0.9987 0.9988 09988 0.9999 0.99890998909990 0.9990 0.990) 0.9991 0.0091 (09 0 0092 0. 2 0.9992 D.0992 0.9993 0.9993 0.9993 0.9993 0.9991 0.9994 09994 0.9901 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.0095 0.9796 0.9996 0.9996 0.9996 D.9906 0.9906 0.099 0.9997 0.9997 0.9997 0.997 090097 DXIT 0907 09997 0.9997 0.0998 1.8 -1.5 -1.4 -1.3 2.0 2.1 -10 2.4 0.8 07 3.0 0 04 -03 -0.2 01 -00 32 3.3 3.4 Note that the probabilities given in this table represent the area to the LEFT of the 7-score. The area to the RIGHT of a z-score = 1 - the area to the LEFT of the Z-score