Question

Supposc Wall Street sccuritics firms paid out ycar-cnd bonuscs of $125,500 per cmploycc last ycar. We take a sample of cmployces at the ASBE sccuritics firm to scc whether the mcan year-end bonus is different from the reported mean of $125,500 for the population 0.001 You wish to test the following claim (H) at a significance level of a Ho: 125500 Ha: 125500 You believe the population is normally distributed and you know the standard deviation is a = 4300. You obtain a sample mean of 124991.2 for a sample of size n = 35. What is the test statistic for this sample? test statistic= (Report answer accurate to 3 decimal places.) What is the p-value for this sample? p-value (Report answer accurate to 4 decimal places.) The p-value is.. less than (or cqual to) a greater than a This test statistic leads to a decision to... reject the nul accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not cqual to 125500. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 125500 The sample data support the claim that the population mean is not equal to 125500.

Answer 1

For the given hypotheses the test statistic is calculated as

$Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{124991.2-125500}{\frac{4300}{\sqrt{4300}}}=-0.700$

The P-value is computed using the Z table shown below and using at Z calculated above as

P-value=0.4839

so,

The P-value=0.4839> 0.01 hence

P-value is greater than alpha.

Decision:

Since the P-value > 0.01 hence we Fail to reject the Null Hypothesis.

Conclusion:

Since we fail to reject the null hypothesis hence there is not sufficient evidence to warrant the rejection of the claim.

Z table:

Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores 0.00 0.5000 05398 0.03 0.5120 0.04 0.09 0.5359 0,00 0,06 0.5239 0.02 0.08 001 003 D.04 0,05 0.06 0.07 0,08 0.09 001 0.02 0,05 0.07 7 0,0002 0,0003 .0004 0.0006 0,0003 00 0.5040 0.5080 0.5199 0.5279 D.5675 0.6064 0.5319 -34 0,0003 0.0003 0.0003 0.0003 0.0003 00003 0.0003 0.5160 0.0005 0.0007 0.5438 0.5753 -3.3 0.0005 0.0005 0,0004 0,0004 00004 0.0004 0.0O04 0.0005 0.0007 0.0010 0.0014 D.D003 0.1 0.5478 0.5517 0.5557 0.5596 D5636 0.5714 -3.2 0.0007 0.0006 0.0009 0.0006 0,0006 00006 0.0005 0,0005 0,2 0.5793 0.5832 0.5871 0,5910 0.5948 0.587 0.6026 0.6103 0,6141 -3.1 0.0010 0.6517 0,6879 0.7224 D.DO09 a.0009 0.0008 0.0008 0.0008 00008 D.DO07 D.0010 0.0014 0.3 0.6179 0.6217 0.6255 0.6293 0,633 0.6368 D.6406 D.6443 0.6480 0,6554 0.6915 O0011 0.0015 06591 0,6950 -3.0 0.0013 0.D013 0.0013 0,0018 .0012 0.0012 0.0016 0.0011 0.0011 0.4 0.6628 0.6664 0.7019 0.6700 0.6736 0.7088 06772 0.7123 D.6808 0.6844 -2.9 0.0019 0,0018 0.0017 0.0016 0.0015 0,5 0,6985 07054 0.7157 0.7190 0.7517 D.0025 0.0034 0.0045 O7389 0.7704 0.7995 D.7486 0.7794 0.8078 DS340 D.8577 D8790 2.8 0.0026 0.0024 a.0023 0,0023 0.0031 0,0041 0.0022 0.0030 0,0040 O0021 0.0021 0.0020 D.DO19 0.6 0.7257 0.729 0.7324 0.7357 07422 D.7454 0.7549 0.7852 0.8133 0.7823 0.8106 -2.7 -2.6 0.0035 0 0017 0.0033 0,0044 0.0032 0.0029 00039 0.0028 0.0038 0.005 0.0027 0.0026 0.0036 0.7 0.8 0.7580 0.7881 0.7611 0.7910 0.7642 0.7673 0,7967 0.7734 0.8023 0.7764 0.805 0.0043 0.0037 0.7930 1 08389 0.8621 0.8159 0.8413 -25 0.0062 D.DO60 0.0059 a.0057 0.0055 0.0073 0.0054 00052 0.0049 D.D048 0.9 0.8186 0.8212 0,8238 .8264 0.8289 D8315 0.8365 0.8599 0.8810 0.0080 -24 0.0082 0,0078 0.0102 0.0075 0.0071 00059 0.0068 0.0066 0.0064 1.0 0.8438 a5665 0.8869 0.9049 0,8461 0.8485 0.8508 0.8531 0.3749 0.8554 03770 0.0107 0.0139 0.0179 0.009 0.8643 23 0.0104 a.0099 0.0096 0,0004 0.0122 0.0158 0.0089 0.0087 D.0O84 0.8686 0.8708 O.8725 0.8830 0.0136 0.0174 -2.2 -2.1 0.0132 0.0170 0.0129 0,0166 0,0125 0.0162 0.0110 0.0143 1.2 1.3 0.8907 0,9082 O.8925 0.8944 0.9115 0.8997 0,9015 00119 0.0116 0.0113 0.8849 0.8888 0.8962 0.913 09279 0.8980 00154 0.0150 0.0146 0.9032 0.9066 0.9147 0.9162 0.9177 09099 0,9222 0,9357 0,9474 0.9573 0.9656 0.9207 0,9236 0.9370 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 00250 00314 0.0192 0.0188 0.0183 1.4 0.9192 0.9332 09251 0.9265 D.9292 0.9306 0.9319 0.9429 0.9535 0.9625 0.0287 0.0359 0.0256 0.0239 0.0233 1.5 0.9382 D.9418 D.9525 0,9441 -1.9 0.0281 0.0274 0,0268 0,0262 0.0244 0.9345 0.9394 0.9505 0.9599 0.9406 0.00 0.0329 0.0294 D.067 -L.8 0.035 0.0436 0.0344 0.0336 0.0322 0.007 1.6 0,9452 0.9554 0.9463 0,9484 09495 0.9515 0,9545 0.040 00495 0.0375 0,0465 0.057 0.9582 -1.7 0.0446 0.0427 0,0418 0,0409 00392 0.0384 1.7 0.9564 09591 0.9608 0.9616 0,9633 0048s 00594 0.0455 0.0559 09686 0.9750 0.0548 0.0526 0.0516 0.0475 0,9649 0.9706 16 0.0537 00505 1.8 0.9641 0,9664 09671 0.9678 0.9693 0.9699 0.9761 0.9812 0.9854 0.0668 0.0655 0,0643 0.0630 0.0618 0,0606 0.0582 1,9 09713 0,9719 0.9726 0,9732 09738 09744 0.9756 0,9767 -1.5 O0721 00869 0.1038 0.0708 0.0853 0.0808 D.U793 U.U778 14 .0764 .0749 0.0735 0.0694 D.0681 2,0 0,9772 0.9778 0.9783 0.9788 0.9793 09798 0.9803 D.98U8 0.9817 0.0968 0.1151 01357 0.1587 0.184 0.9834 0,987 -1.3 0.0918 0.0823 0.9826 09838 0.9857 0.0951 0.0934 0.0901 0.0885 0.0838 2.1 0.9821 0.9830 0.9842 0,9878 0.9846 D.9850 0.1020 0.1210 0988 0,9864 0,9868 -1.2 0.1131 0.1112 0,1093 0.1075 0.1056 0.125 0.1003 D.0985 2.2 0.9861 0.9875 0.9884 0.9887 0,9890 0.9901 0.9925 0.9906 0.9929 -1.1 0.1335 01314 .1292 0.1271 0.1492 O1230 0.1190 D.1170 23 0.9893 0,9806 0.9898 09904 0.9927 0.9909 0.9911 0.9913 0,9916 0.140 0993 0.9922 -10 0.1562 0.1539 0.1515 0.1469 0.1446 0.1423 0.1379 2.4 0.9918 0.9920 0.9940 09935 0.9932 0.9934 0.995 0.9936 0.1814 0.9946 -09 0.1788 a.1762 .1736 0.1711 0.1977 0.2266 O1685 0.1660 D.1635 D.1611 D.1867 2.5 0.9938 0.9941 0,9943 09945 0.9948 0.996 0.9971 D.9949 0.9952 0.2061 0.2358 0.9957 0,9968 0.9953 0.9965 D.9962 O.8 0.2119 0.2090 0.2033 0.2327 0.2005 0.2296 O.1949 0.1922 0.1894 2.6 0,9956 09959 0.9960 0.9963 0.9964 0.9967 0.9972 09973 D.9979 0.9985 0.9989 -07 0.2420 0.2389 02236 0.2206 0.2177 0.2148 D.245 0.2776 0.3121 2.7 0,9966 09969 0.9970 0,9974 0.2578 0.2912 0.3264 06 0.2743 0.2709 0.2676 d.2643 0.2611 02546 02514 0.2483 2.8 0.9974 0.9975 0.9976 0.9977 09977 0.9978 D.9979 0.9980 0.998 0.9984 0.9989 0.9981 0.9987 0,9982 0,9987 0.9985 0.9989 -05 -04 0.3085 0.34-16 0.3050 0.3409 D.3783 0.3015 0.3372 0,2981 0,3336 0.2946 0.3300 02877 03228 0.2843 0.3192 0.2810 0.3156 2,9 3.0 0.9982 0.9987 0,999 0.9983 0,9988 09984 0,9988 0.9986 0.9990 0.9986 0,9990 03 0.3821 0.3745 0.4129 g.3707 0.3669 0,4052 0.3632 03594 0.3557 0.3936 04325 0.3520 D.3483 3.1 0.9990 0.9991 0.9993 0.9991 09992 0.9992 09992 D.9992 0.9993 0.9993 0.9991 0,9995 -02 0.4207 04602 0.4168 0,4090 0,4013 0.3974 0.3897 0.3859 3.2 0.9993 0,9994 0.9994 09994 0.9994 09996 0.9995 0.9995 0,9995 0.4562 0.4522 0.4483 04443 04404 04364 0.4286 04247 3.3 .9995 0,9995 0.9996 09996 0.9996 D.9996 0.9996 0.9997 0480 0476 D468 0.4840 0,9997 D.9997 0.500 0.4960 0 4920 0.4880 0.4721 D4641 3.4 0.9997 0,9997 0,9997 09997 0.9997 09997 0.9997 0.9998 Note that the probabilities given in this table represent the area to the LEFT of the z-score. The area to the RIGHT of a z-score 1- the area to the LEFT of the z-score