The expected average of concrete compression tests is 5000 psi. Given a set of d

Question

The expected average of concrete compression tests is 5000 psi. Given a set of data the actual average is 6000 psi. The standard deviation is 500 psi. Fifteen (15) samples have been taken. Can we be 90% confident that the samples represent the actual mean? Use t-table below.

t Table cum. prob 50 75 .80 .85 90 95 .975 .99 .995 9995 one-tail0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005 two-tails1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001 df 1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.8263.66 318.31 636.62 2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599 3 0.000 0.765 0.978 1250 1638 2.353 3.182 4.54 5.841 10.215 12.924 4 0.000 0.74 0.941 .190 1.533 2.132 2.7763.747 4.604 7.173 8.610 5 0.000 0.727 0.920 156 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 71 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.000 0.706 0.889 1.108 1.397 .860 2.306 2.896 3.355 4.501 5.041 9 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.000 0.697 0.876 1.088 1.363 1.7962.201 2.718 3.106 4.025 4.437 12 0.000 0.695 0.873 1.083 1.356 1782 2.1792.681 3.055 3.930 4.318 130.000 0.6940.870 1.079 .3501771 2.160 2.650 3.012 3.852 4.221 14 0.000 0.692 0.868 1.076 .345 1.761 2.145 2.624 2.977 3.787 4.140 150.000 0.69 0.866 1.074 .34 1.753 2.131 2.602 2.947 3.733 4.073 16 0.000 0.690 0.865 1.071 1.3371.746 2.120 2.583 2.921 3.686 4.015 171 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 0.000 0.688 0.862 1067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.000 0.687 0.860 1.064 325 1.725 2.086 2.528 2.845 3.552 3.850 210.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.000 0.686 0.858 .061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 230.000 0.685 0.858 1.060 319 1.714 2.069 2.500 2.807 3.485 3.768 24 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 0.000 0.684 0.856 1.058 .316 1.708 2.060 2.485 2.787 3.450 3.725 26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 271 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.690 28 0.000 0.683 0.855 1.056 313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.000 0.683 0.854 1.055 311 1.699 2.045 2.462 2.756 3.396 3.659 30 0.000 0.683 0.854 1.055 .310 1.697 2.042 2.457 2.750 3.385 3.646 40 0.000 0.680.851 1.050 .303 1.684 2.02 2.423 2.704 3.307 3.551 60 0.000 0.679 0.848 .045 1.296 1.671 2.000 2390 2.660 3.232 3.460 80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639 3.195 3.416 100 0.000 0.677 0.845 1.042 1.290 1.660 .984 2.364 2.626 3.174 3.390 10000.000 0.675 0.842 1.0371.282 1.646 1.962 2.330 2.58 3.098 3.300 Z 0.000 0.674 0.842 .036 1.282 1.645 1.960 2.326 2.576 3.090 3.291 0% 50% 60% 70% 80% 90% 95% 98% 99% 99.8% 99.9% Confidence Level

Explanation / Answer

For 90 percent confidence level Z= 1.645

Now actual strength = target strength +- Z* standard deviation

Expected average = 5000 psi

Actual average = 6000 psi

Target strength = 5000 psi

Actual upper limit = 5000 + 1.645* 500 = 5822.5 psi

Since our actual strength is more than upper limit thus we can be more than 90 percent sure that the samples represent actual mean

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