An educational researcher says that the proportion of college students who study for their statistics final exam is 68%. Write the claim, null and alternative hypotheses for this statement. Draw a distribution to represent it, and then identify the type of test (tail) that should be used.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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An educational researcher says that the proportion of college students who study for their statistics final exam is 68%. Write the claim, null and alternative hypotheses for this statement. Draw a distribution to represent it, and then identify the type of test (tail) that should be used.
A24
c is a confidence level
Appendix II
One-tail area
Left-tail
area
Two-tail area
-t
0
0
0
Area
0
TABLES
Right-tail
area
CARSTUEN
t
TABLE Critical Values for Student's t Distribution
0.250 0.125 0.100 0.075
0.500 0.250 0.200 0.150
0.500 0.750 0.800 0.850
one-tail area.
two-tail area
d.f.
1
2
00
3
4
12.924
8.610
6.869
5.959
5.408
5.041
4.781
4:587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
1.000 2.414 3.078 4.165 6.314 12.706 31.821 63.657 636.619
0.816 1.604 1.886 2.282 2.920 4.303 6.965 9.925 31.599
0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841
0.741 1.344 1.533 1.778 2.132 2.776 3.747 4.604
0.727 1.301 1.476 1.699 2.015 2.571 3.365 4.032
0.718 1.273 1.440 1.650
1.650 1.943 2.447 3.143 3.707
65 5.4
0.711 1.2541 1.415 1.617 1.895 2.365 2.998 3.499
Lore
0.706 1.240 1.397 1.592 1.860 2.306 2.896 3.355
0.703 1.230 1.383
1.383 1.574 1.833 2.262- 2.821 3.250
0.700 1.221 1.372 1.559
1.559 1.812 2.228
1.812 2.228 2.764 3.169
0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106
0.695 1.209 1.356 1.538 1.782 2.179 2.681 3.055
0.694 1.204 1.350 1.530 1.771 2.160 2.650 3.012
0.692 1.200 1.345 1.523 1.761 2.145 2.624 2.977
0.691 1.197 1.341 1.517 1.753 2.131 2.602 2.947
0.690 1.194 1.337 1.512 1.746 2.120 2.583 2.921
0.689 1.19
1.191 1.333 1.508 1.740 2.110 2.567 2.898
0.688 1.189 1.330 1.504 1.734 2:101, 2.552 2.878
0.688 1.187 1.328 1.500 1.729 2.093 2.539 2.861,
0.687 1.185 1.325 1.497 1.725 2.086 2.528 2.845
0.686 1.183 1.323 1,494 1.721 2.080
2.080 2.518
2.518 2.831
0.686 1.182 1.321 1.492
1.717 2.074 2.508 2.819
0.685 1.180 1.319 1.489 1.714 2.069
2.069 2.500 2.807
0.685 1.179.
1.179. 1.318 1.487 1.711 2.064 2.492 2.797
0.684 1.198 1.316 1.485 1.708 2.060 2.485 2,787
0.684 1.177 1.315 1.483 1.706 2.056 2.479 2.779
0.684 1.176 1.314
0.683 1.175
1.175 1.313 1.480. 1.701 2.048 2.467 2.763
0.683 1.174 1.311 1.479 1.699 2.045 2462 2.756
0.683 1.173 1.310 1.477 1,697 2.042 2.457 2.750
0.682 1.170 1.306
1.690 2.030 2.438 2.724
0.681, 1.167 1.303 1.468 1.684 2.021 2.423 2.704
0.680 1.165 1.301 1.465 1.679 2.014 2.412 2.690
0.679 1.164 1.299 1.462 1.676 2.009 2.403 2.678
0.679 1.162 1.296 1.458 1.671 2.000 2.390
2.390 2.660
0.678 1.160 1.294
0.678 1.159 1.292
0.677 1.157 1.290 1.451 1.660 1.984 2.364 2.626
0.675 1.152
1.152 1.283 1.442 1.648 1.965 2,334 2.586
0.675 1.151 1.282 1.441 1.646 1.962 2.330 2.581
330 2.58
1.482 1.703 2.052
2052 2.473 2.7
Syn
1.472
1.456 1.667 1.994 2.381 2.648
1,453 1.664 1.990 2.374 2.639
646 1,96
0.674 1.150 1.282 1.440 1.645 1.960
For degrees of freedom d.f. not in the table, use the closest d.f. that is smaller.
5
6
7
8
9
10
11
12
13
14
15
16.
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
.60
70
80
100
500
1000
C
0.025 0.010 0.005
0.050
0.100 0.050 0.020
0.100
0.900 0.950 0.980 0.990 0.999
0.020 0.010
0.0010
..
0.0005
2.576
2.326
3,883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.690
3.674
3.659
3,646
3.591
3.551
3.520
3.496
3.460
3.435
3.416
3.390
3.310
3,300
3.291
Transcribed Image Text:A24 c is a confidence level Appendix II One-tail area Left-tail area Two-tail area -t 0 0 0 Area 0 TABLES Right-tail area CARSTUEN t TABLE Critical Values for Student's t Distribution 0.250 0.125 0.100 0.075 0.500 0.250 0.200 0.150 0.500 0.750 0.800 0.850 one-tail area. two-tail area d.f. 1 2 00 3 4 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4:587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 1.000 2.414 3.078 4.165 6.314 12.706 31.821 63.657 636.619 0.816 1.604 1.886 2.282 2.920 4.303 6.965 9.925 31.599 0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841 0.741 1.344 1.533 1.778 2.132 2.776 3.747 4.604 0.727 1.301 1.476 1.699 2.015 2.571 3.365 4.032 0.718 1.273 1.440 1.650 1.650 1.943 2.447 3.143 3.707 65 5.4 0.711 1.2541 1.415 1.617 1.895 2.365 2.998 3.499 Lore 0.706 1.240 1.397 1.592 1.860 2.306 2.896 3.355 0.703 1.230 1.383 1.383 1.574 1.833 2.262- 2.821 3.250 0.700 1.221 1.372 1.559 1.559 1.812 2.228 1.812 2.228 2.764 3.169 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 0.695 1.209 1.356 1.538 1.782 2.179 2.681 3.055 0.694 1.204 1.350 1.530 1.771 2.160 2.650 3.012 0.692 1.200 1.345 1.523 1.761 2.145 2.624 2.977 0.691 1.197 1.341 1.517 1.753 2.131 2.602 2.947 0.690 1.194 1.337 1.512 1.746 2.120 2.583 2.921 0.689 1.19 1.191 1.333 1.508 1.740 2.110 2.567 2.898 0.688 1.189 1.330 1.504 1.734 2:101, 2.552 2.878 0.688 1.187 1.328 1.500 1.729 2.093 2.539 2.861, 0.687 1.185 1.325 1.497 1.725 2.086 2.528 2.845 0.686 1.183 1.323 1,494 1.721 2.080 2.080 2.518 2.518 2.831 0.686 1.182 1.321 1.492 1.717 2.074 2.508 2.819 0.685 1.180 1.319 1.489 1.714 2.069 2.069 2.500 2.807 0.685 1.179. 1.179. 1.318 1.487 1.711 2.064 2.492 2.797 0.684 1.198 1.316 1.485 1.708 2.060 2.485 2,787 0.684 1.177 1.315 1.483 1.706 2.056 2.479 2.779 0.684 1.176 1.314 0.683 1.175 1.175 1.313 1.480. 1.701 2.048 2.467 2.763 0.683 1.174 1.311 1.479 1.699 2.045 2462 2.756 0.683 1.173 1.310 1.477 1,697 2.042 2.457 2.750 0.682 1.170 1.306 1.690 2.030 2.438 2.724 0.681, 1.167 1.303 1.468 1.684 2.021 2.423 2.704 0.680 1.165 1.301 1.465 1.679 2.014 2.412 2.690 0.679 1.164 1.299 1.462 1.676 2.009 2.403 2.678 0.679 1.162 1.296 1.458 1.671 2.000 2.390 2.390 2.660 0.678 1.160 1.294 0.678 1.159 1.292 0.677 1.157 1.290 1.451 1.660 1.984 2.364 2.626 0.675 1.152 1.152 1.283 1.442 1.648 1.965 2,334 2.586 0.675 1.151 1.282 1.441 1.646 1.962 2.330 2.581 330 2.58 1.482 1.703 2.052 2052 2.473 2.7 Syn 1.472 1.456 1.667 1.994 2.381 2.648 1,453 1.664 1.990 2.374 2.639 646 1,96 0.674 1.150 1.282 1.440 1.645 1.960 For degrees of freedom d.f. not in the table, use the closest d.f. that is smaller. 5 6 7 8 9 10 11 12 13 14 15 16. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 35 40 45 50 .60 70 80 100 500 1000 C 0.025 0.010 0.005 0.050 0.100 0.050 0.020 0.100 0.900 0.950 0.980 0.990 0.999 0.020 0.010 0.0010 .. 0.0005 2.576 2.326 3,883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3,646 3.591 3.551 3.520 3.496 3.460 3.435 3.416 3.390 3.310 3,300 3.291
A22
The table entry for z is the area to the
left of z.
Appendix II
NUP continued
(b) Confidence Interval
Critical Values a
Level of
Confidence c
0.70, or 70%
0.75, or 75
0.80, or 80%
0.85, or 85%
0.90, or 90%
0.95, or 95%
0.98, or 98%
0.99, or 9996
Critical
Value z
1.04
1.15
1.28
1.44
1.645
1.96
2.33
2.58
Appendix II TABLES
The table entry for z is the area to the
left of z.
Tables
continued
z
.00
.02 .03 .04 05
..07
0.0
5239
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
12
.01
09
5000 5040 5080 5120 5160 5199 5239 5279 5319 5359
5398 5438
5438 5478
5478 5517 5557 5596 5636 5675 5714 5753
5793 5832
5832 5671 5910 5948 5987 6025 6064 6103
6141
.6179 6217 6255
6255 6293 6331 6368 6405 6443 6480 5517
6554 6591 6628 6664 6700 6736 6772 6808 6844 6879
6915 6950 6985 7019
7054 7088 7123 7157 7190 7224
7257 7291 7324 7357 7389 7422 7454 7486 7517 7549
7580 7611 7642 7673 7704 7734 7764 7794 7823 7852
7881 7910 7939 7967 7995 8025 8051 9078 8106
8106 8133
8159 8186 8212 8238 8264 8289 8315 0340 8565 8389
8413 8438 8461 8485 8508 8531 8554 8577 8599 8621
8643 8665 8686 8708
8729 8749 8770 8790 8810 8850
8849 8859 8688 8907 8925 8944 8962 8980
8962 8980 8997
8997 9015
9032 9049 9066 9082 9099 9115 9131
9147 9162 9177
9192 9207 9222 9256 9251 9265 9279 9292 9306 9319
9332 9345 9357 9570 9562 9594 9406 9418 9429 9441
9382
1.6 9452 9463 9474 9484 9495 9505 9515
1.7 9554 9564 9575 9582 9591 9599 9608
18 9641 9649 9656 9664 9671 9678 9686
1.9 9713 9719 9726 9732 9758 9744 9750
2.0 9772 9778 9783 9788
9788 9793 9798 9803 9808 9812 9817
2.1
9821 9826 9830 9834 9838 9842 9046 9850 9854 9857
9861 9864 9868 9871 9875 9878 9881 9884 9887 9890
9893 9896 9898 9901 9904 9906 9909 9911 9913 9916
9918 9920 9922 9925 9927 9929 9931 9932 9934 9936
.9938 9940 9941 9943 9945 9946 9918 9949 9951 9952
9957 9959 9960 9961 9962 9963 9964
9968 9969 9970 9971 9972 9973 9974
9977 9977 9978 9979 9979 9980 9981
1.3
1.4
15
9525 9535 9545
9616 9625 9633
9695 9699 9706
5756 9761 9767
2.2
2.3
24
9953 9955 9956
2.5
26
27 9965 9966 9967
2.8 9974 9975 9976
29 9981 9982 9982
9982 9983
3.0
3.1
9983 9984 9984 9985 9985 9986 9986
9987
9987 9987
9990 9991
9993 9993
9995 9995 9995 9996 9996 9996 9995 9996 9996 9997
9987 9988 9988 9989 9989 9989 9990 9990
9991 9991 9992 9992 9992 9992 9993 9993
9994 9994 9994 9994 9994 9995 9995 9995
3.2
3.3
3.4 9997 9997 9997 9997 9997 9997 9997 9997 9997 9998
for values gater than 3.49, use 1000 to approximate the ar
A
continued
(c) Hypothesis Testing, Critical Values zo
Level of Significance
3-09
Critical value to for a left-tailed test
Critical value o for a right-tailed test
Critical values o for a two-tailed test
-0.05
-1.645
1.645
1.96
.06
1251
1469
-0.01
-2.33
2.33
#258
TABLE 5 Areas of a Standard Normal Distribution
(a) Table of Areas to the Left of z
08 09
2 00 01 02 03 04
-3.4 0005 0003 0003
-3.3 0005 0005 0005 0004 0004 0004 0004 0004 0004 0003
-3.2 0007 0007 0006 0006 0006 0006 0006 0005 0005 0005
06 .07
05
0003 0003 0005 0003 0003 0005 0002
.0008
-3.1 0010 0009 0009 0009 0006 0008 0000
0007 0007
-30 0013 0013 0013 0012 0012
0011 0011 0011 0010 0010
-29 0019 0018 0018 0017 0016 0016 0015 0015 0014 0014
0025 0024
-28 0026
0022 0021
0024 0025 0023
0021 0020 0019
-27 0035 0034 0033 0032 003) 0030 0029 0028 0027 0026
-26 0047 0045 0044 0045 0041 00400039
0039 0038 0037 0036
-2.5 0062
0059 0057 0055
0055 0054 0052 0051 0049 0048
-2.4 0082 0080 0078
0075 0073 0071 0069 0068 0066 0064
-2.3 0107 0104 0102 0099 0096 0094 0091 0089 0087 0064
-22 0139 0136 0132
0132 0129 0125 0122 0119 0116 0113 0110
0166 0162 0158 0154
0212 0207 0202 0197
0268 0262 0256 0250
0336 0329 0322 0314 0307 0301 0294
0384 0575 0367
0150 0146 0143
0192 0188 0183
0244 0239 0233
-21 0179 0174 0170
-20 0228 0222 0217
-1.9 0267 0281 0274
18 0359 0351 0344
1.7 0446 0436 0427 0418 0409 04010392
1.6 0548 0537 0526 0516 0505 0495 0485
-15 0668 0655 0643 0630 0618 0606 0594
-1.4 0808 0793 0778 0764 0749 0735
0735 0721
0918 0901 0885 0869 08535 0858 0823
1056 1038 1020 1003 0985
0475 0465 0455
0582 0571 0559
0708 0694 0681
-1.3 0968 0951 0934
1112 1093 1075
-1.2 1151 1151
1357 1355
-1.1
-1.0 1587
1355
1314
1539
1271
1492
1190 1170
1401 1379
1292
1562
1515
1841
1841 1814 1788 1762 1736 1201 1685 1600 1635 1611
2053 2005 1977 1949 1922 1894 1867
-0.8 2119
2119 2000 2061
2090 2061
-07 2420 2389 2358 2127 2296 2266 2236 2206 2177 2148
-0.6 2743 2709 2676 2645 2611 2578 2546 2514 2483 2451
-0.5 3085 5050 3015 2981 2946 2912 2877 2843 2810 2776
-0.4 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121
3783 3745 3707
-0.3 3821
3669 3632 3594 3557 3520 3483
-0.2 4207 4168 4129 4090 4052 4013 3974 3936 3897 3859
-0.1 4602 4562 4522 4483 4443
4443 4404 4364 4325
-0.0 5000 4960 4920 4880 4840
4840 4801 4761 4721
for values of less than -3.49, use 0.000 to approximate the
4286 4247
4681 4641
08
1230 1210
1446 1423
A23
Transcribed Image Text:A22 The table entry for z is the area to the left of z. Appendix II NUP continued (b) Confidence Interval Critical Values a Level of Confidence c 0.70, or 70% 0.75, or 75 0.80, or 80% 0.85, or 85% 0.90, or 90% 0.95, or 95% 0.98, or 98% 0.99, or 9996 Critical Value z 1.04 1.15 1.28 1.44 1.645 1.96 2.33 2.58 Appendix II TABLES The table entry for z is the area to the left of z. Tables continued z .00 .02 .03 .04 05 ..07 0.0 5239 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 12 .01 09 5000 5040 5080 5120 5160 5199 5239 5279 5319 5359 5398 5438 5438 5478 5478 5517 5557 5596 5636 5675 5714 5753 5793 5832 5832 5671 5910 5948 5987 6025 6064 6103 6141 .6179 6217 6255 6255 6293 6331 6368 6405 6443 6480 5517 6554 6591 6628 6664 6700 6736 6772 6808 6844 6879 6915 6950 6985 7019 7054 7088 7123 7157 7190 7224 7257 7291 7324 7357 7389 7422 7454 7486 7517 7549 7580 7611 7642 7673 7704 7734 7764 7794 7823 7852 7881 7910 7939 7967 7995 8025 8051 9078 8106 8106 8133 8159 8186 8212 8238 8264 8289 8315 0340 8565 8389 8413 8438 8461 8485 8508 8531 8554 8577 8599 8621 8643 8665 8686 8708 8729 8749 8770 8790 8810 8850 8849 8859 8688 8907 8925 8944 8962 8980 8962 8980 8997 8997 9015 9032 9049 9066 9082 9099 9115 9131 9147 9162 9177 9192 9207 9222 9256 9251 9265 9279 9292 9306 9319 9332 9345 9357 9570 9562 9594 9406 9418 9429 9441 9382 1.6 9452 9463 9474 9484 9495 9505 9515 1.7 9554 9564 9575 9582 9591 9599 9608 18 9641 9649 9656 9664 9671 9678 9686 1.9 9713 9719 9726 9732 9758 9744 9750 2.0 9772 9778 9783 9788 9788 9793 9798 9803 9808 9812 9817 2.1 9821 9826 9830 9834 9838 9842 9046 9850 9854 9857 9861 9864 9868 9871 9875 9878 9881 9884 9887 9890 9893 9896 9898 9901 9904 9906 9909 9911 9913 9916 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936 .9938 9940 9941 9943 9945 9946 9918 9949 9951 9952 9957 9959 9960 9961 9962 9963 9964 9968 9969 9970 9971 9972 9973 9974 9977 9977 9978 9979 9979 9980 9981 1.3 1.4 15 9525 9535 9545 9616 9625 9633 9695 9699 9706 5756 9761 9767 2.2 2.3 24 9953 9955 9956 2.5 26 27 9965 9966 9967 2.8 9974 9975 9976 29 9981 9982 9982 9982 9983 3.0 3.1 9983 9984 9984 9985 9985 9986 9986 9987 9987 9987 9990 9991 9993 9993 9995 9995 9995 9996 9996 9996 9995 9996 9996 9997 9987 9988 9988 9989 9989 9989 9990 9990 9991 9991 9992 9992 9992 9992 9993 9993 9994 9994 9994 9994 9994 9995 9995 9995 3.2 3.3 3.4 9997 9997 9997 9997 9997 9997 9997 9997 9997 9998 for values gater than 3.49, use 1000 to approximate the ar A continued (c) Hypothesis Testing, Critical Values zo Level of Significance 3-09 Critical value to for a left-tailed test Critical value o for a right-tailed test Critical values o for a two-tailed test -0.05 -1.645 1.645 1.96 .06 1251 1469 -0.01 -2.33 2.33 #258 TABLE 5 Areas of a Standard Normal Distribution (a) Table of Areas to the Left of z 08 09 2 00 01 02 03 04 -3.4 0005 0003 0003 -3.3 0005 0005 0005 0004 0004 0004 0004 0004 0004 0003 -3.2 0007 0007 0006 0006 0006 0006 0006 0005 0005 0005 06 .07 05 0003 0003 0005 0003 0003 0005 0002 .0008 -3.1 0010 0009 0009 0009 0006 0008 0000 0007 0007 -30 0013 0013 0013 0012 0012 0011 0011 0011 0010 0010 -29 0019 0018 0018 0017 0016 0016 0015 0015 0014 0014 0025 0024 -28 0026 0022 0021 0024 0025 0023 0021 0020 0019 -27 0035 0034 0033 0032 003) 0030 0029 0028 0027 0026 -26 0047 0045 0044 0045 0041 00400039 0039 0038 0037 0036 -2.5 0062 0059 0057 0055 0055 0054 0052 0051 0049 0048 -2.4 0082 0080 0078 0075 0073 0071 0069 0068 0066 0064 -2.3 0107 0104 0102 0099 0096 0094 0091 0089 0087 0064 -22 0139 0136 0132 0132 0129 0125 0122 0119 0116 0113 0110 0166 0162 0158 0154 0212 0207 0202 0197 0268 0262 0256 0250 0336 0329 0322 0314 0307 0301 0294 0384 0575 0367 0150 0146 0143 0192 0188 0183 0244 0239 0233 -21 0179 0174 0170 -20 0228 0222 0217 -1.9 0267 0281 0274 18 0359 0351 0344 1.7 0446 0436 0427 0418 0409 04010392 1.6 0548 0537 0526 0516 0505 0495 0485 -15 0668 0655 0643 0630 0618 0606 0594 -1.4 0808 0793 0778 0764 0749 0735 0735 0721 0918 0901 0885 0869 08535 0858 0823 1056 1038 1020 1003 0985 0475 0465 0455 0582 0571 0559 0708 0694 0681 -1.3 0968 0951 0934 1112 1093 1075 -1.2 1151 1151 1357 1355 -1.1 -1.0 1587 1355 1314 1539 1271 1492 1190 1170 1401 1379 1292 1562 1515 1841 1841 1814 1788 1762 1736 1201 1685 1600 1635 1611 2053 2005 1977 1949 1922 1894 1867 -0.8 2119 2119 2000 2061 2090 2061 -07 2420 2389 2358 2127 2296 2266 2236 2206 2177 2148 -0.6 2743 2709 2676 2645 2611 2578 2546 2514 2483 2451 -0.5 3085 5050 3015 2981 2946 2912 2877 2843 2810 2776 -0.4 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121 3783 3745 3707 -0.3 3821 3669 3632 3594 3557 3520 3483 -0.2 4207 4168 4129 4090 4052 4013 3974 3936 3897 3859 -0.1 4602 4562 4522 4483 4443 4443 4404 4364 4325 -0.0 5000 4960 4920 4880 4840 4840 4801 4761 4721 for values of less than -3.49, use 0.000 to approximate the 4286 4247 4681 4641 08 1230 1210 1446 1423 A23
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