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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 sxs 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. a=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, p = 0.0210 (Round to four decimal places as needed.) For the alternative p = 0.4, ẞ= 0.0484 (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.

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 sxs 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. a=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, p = 0.0210 (Round to four decimal places as needed.) For the alternative p = 0.4, ẞ= 0.0484 (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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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. a = 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, p = 0.0210. (Round to four decimal places as needed.) For the alternative p = 0.4, p = 0.0484. (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.
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. a = 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, p = 0.0210. (Round to four decimal places as needed.) For the alternative p = 0.4, p = 0.0484. (Round to four decimal places as needed.) (c) Is this a good test procedure? Consider a value of a to be relatively small if it is less than 0.1000 and relatively large if it is greater than 0.1000. This a good test procedure, because while a is relatively small, at least one ẞ is relatively large. while both values of ẞ are relatively small, a is relatively large. all values of a and ẞ are relatively large. all values of a and ẞ are relatively small.
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 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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 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