Question

A decade-old study found that the proportion, p. of high school seniors who believed that "getting rich was an important personal goal was 75%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 215 high school seniors in Ns random sample, 148 believe that "getting rich" is an important goal. Can he conclude, at the 0.1 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consulta Ist of formulas.) The run hypothesis: The alternative hypothesis: The type of test statistic The value of the test statistics (Round to at least three decimal place) X 5 2 The value: (Round to at least three decimal places) Can we conclude that the proportion of high school seniors who believe that getting rich is an important goalhas changed?

Answer 1

The Hypotheses are:

Ho:p=0.75

Ha :p +0.75

# It is two tailed test from the hypotheses we can say.

#The test statistic is calculated as:

1) - 帶 -0.75 215

The P-value:

P-value computed from Z table shown below as:

P-value=0.038.

Conclusion:

Since |Z| > Z _0.05 =1.645 and P-value <0.1 hence we reject the null hypothesis and yes we conclude that there is enough to support the Claim.

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