The proportion of adults living in a small town who are college graduates is estimated to be p = 0.3. To test this hypothesis, a random sample of 200 adults is selected. If the number of college graduates in the sample is anywhere in the fail-to-reject region defined to be 52≤x≤68, where x is the number of college graduates in our sample, we shall not reject the null hypothesis that p = 0.3; otherwise, we shall conclude that p 0.3. Complete parts (a) through (c) below. Use the normal approximation. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Evaluate a assuming that p = 0.3. x= 0.1896 (Round to four decimal places as needed.) (b) Evaluate ẞ for the alternatives p = 0.2 and p = 0.4. For the alternative p = 0.2, ẞ= ☐ (Round to four decimal places as needed.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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I need help with part b please

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.3. To test
this hypothesis, a random sample of 200 adults is selected. If the number of college graduates in the sample is
anywhere in the fail-to-reject region defined to be 52 ≤x≤ 68, where x is the number of college graduates in
our sample, we shall not reject the null hypothesis that p = 0.3; otherwise, we shall conclude that p = 0.3. Complete
parts (a) through (c) below. Use the normal approximation.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) Evaluate a assuming that p = 0.3.
α= 0.1896 (Round to four decimal places as needed.)
(b) Evaluate ẞ for the alternatives p = 0.2 and p = 0.4.
For the alternative p = 0.2, ẞ= (Round to four decimal places as needed.)
Transcribed Image Text:The proportion of adults living in a small town who are college graduates is estimated to be p = 0.3. To test this hypothesis, a random sample of 200 adults is selected. If the number of college graduates in the sample is anywhere in the fail-to-reject region defined to be 52 ≤x≤ 68, where x is the number of college graduates in our sample, we shall not reject the null hypothesis that p = 0.3; otherwise, we shall conclude that p = 0.3. Complete parts (a) through (c) below. Use the normal approximation. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Evaluate a assuming that p = 0.3. α= 0.1896 (Round to four decimal places as needed.) (b) Evaluate ẞ for the alternatives p = 0.2 and p = 0.4. For the alternative p = 0.2, ẞ= (Round to four decimal places as needed.)
Areas under the Normal Curve
Areas under the Normal Curve
z
.00
.01
-3.4
0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009 0.0009
-3.0 0.0013 0.0013 0.0013 0.0012
-2.9 0.0019 0.0018 0.0018 0.0017
-2.8 0.0026 0.0025 0.0024 0.0023
-2.7 0.0035 0.0034 0.0033 0.0032
-2.6 0.0047 0.0045 0.0044 0.0043
-2.5 0.0062 0.0060 0.0059 0.0057
-2.4 0.0082 0.0080 0.0078 0.0075
-2.3 0.0107 0.0104 0.0102 0.0099
.02
.03
.05
.04
.06
.07
0.0003 0.0003
0.0003 0.0003
0.0004 0.0004 0.0004 0.0004
0.0006 0.0006 0.0006 0.0005
0.0008 0.0008 0.0008 0.0008
0.0012 0.0011 0.0011 0.0011
0.0016 0.0016 0.0015 0.0015
0.0023 0.0022 0.0021 0.0021
0.0031 0.0030 0.0029 0.0028
.08
.09
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
z
Z
.00
.01
.02
.03
.04
.05
.06
.07
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.3
0.4
-0.3 0.3821 0.3783 0.3745
2
.00
.01
0.0041 0.0040 0.0039 0.0038
0.0055 0.0054 0.0052 0.0051
0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
0.0096 0.0094 0.0091 0.0089 0.0087
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113
-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 -2.0
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571
0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3
0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192
0.3707 0.3669 0.3632 0.3594 0.3557
0.3483 -0.3
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.02
.03
.04
.05
.06
.07
.08
.09
Z
0.0014 0.0014 -2.9
0.0020 0.0019 -2.8
0.0027 0.0026 2.7
0.0037 0.0036 -2.6
0.0049 0.0048 -2.5
0.5
0.0084 -2.3
0.0110 -2.2
0.0143 -2.1
2.7
0.2483 0.2451 -0.6
0.2810
0.2776 -0.5
0.3156
0.3520
0.3121 -0.4
¡A
2
.00
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.6179 0.6217 0.6255
0.6293 0.6331
0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0.9783 0.9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2 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 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
0.9965 0.9966 0.9967
0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992
0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.01
.02
.03
.04
.05
.06
.07
.08
.09
.08
.09
0.5319 0.5359 0.0
2
Z
Transcribed Image Text:Areas under the Normal Curve Areas under the Normal Curve z .00 .01 -3.4 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 -3.2 0.0007 0.0007 0.0006 0.0006 -3.1 0.0010 0.0009 0.0009 0.0009 -3.0 0.0013 0.0013 0.0013 0.0012 -2.9 0.0019 0.0018 0.0018 0.0017 -2.8 0.0026 0.0025 0.0024 0.0023 -2.7 0.0035 0.0034 0.0033 0.0032 -2.6 0.0047 0.0045 0.0044 0.0043 -2.5 0.0062 0.0060 0.0059 0.0057 -2.4 0.0082 0.0080 0.0078 0.0075 -2.3 0.0107 0.0104 0.0102 0.0099 .02 .03 .05 .04 .06 .07 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0006 0.0006 0.0006 0.0005 0.0008 0.0008 0.0008 0.0008 0.0012 0.0011 0.0011 0.0011 0.0016 0.0016 0.0015 0.0015 0.0023 0.0022 0.0021 0.0021 0.0031 0.0030 0.0029 0.0028 .08 .09 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 z Z .00 .01 .02 .03 .04 .05 .06 .07 0.0007 0.0007 -3.1 0.0010 0.0010 -3.0 0.3 0.4 -0.3 0.3821 0.3783 0.3745 2 .00 .01 0.0041 0.0040 0.0039 0.0038 0.0055 0.0054 0.0052 0.0051 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4 0.0096 0.0094 0.0091 0.0089 0.0087 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 -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 -2.0 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 -1.2 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3707 0.3669 0.3632 0.3594 0.3557 0.3483 -0.3 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 .02 .03 .04 .05 .06 .07 .08 .09 Z 0.0014 0.0014 -2.9 0.0020 0.0019 -2.8 0.0027 0.0026 2.7 0.0037 0.0036 -2.6 0.0049 0.0048 -2.5 0.5 0.0084 -2.3 0.0110 -2.2 0.0143 -2.1 2.7 0.2483 0.2451 -0.6 0.2810 0.2776 -0.5 0.3156 0.3520 0.3121 -0.4 ¡A 2 .00 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0.9772 0.9778 0.9783 0.9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 2.2 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 2.3 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .01 .02 .03 .04 .05 .06 .07 .08 .09 .08 .09 0.5319 0.5359 0.0 2 Z
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