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The mean inspection time, using the current method of quality control, has been found over a long period of time to be 160 seconds. Your manager decides to introduce a new method of quality control aimed at reducing this to as short as possible and so she expects the new method to produce a smaller mean. A random sample of measurement of inspection time taken after the new method had become established gave the following distribution:   Time (sec) 120 129 135 144 157 173 179 191 Number 1 3 2 3 4 3 3 4   Your manager thinks that the introduction of the new method of inspection has been very                                          effective in reducing the inspection time. Using the data provided and assuming the inspection time to be normally distributed with a standard deviation of 28 seconds, test this hypothesis at 5% level of significance

The mean inspection time, using the current method of quality control, has been found over a long period of time to be 160 seconds. Your manager decides to introduce a new method of quality control aimed at reducing this to as short as possible and so she expects the new method to produce a smaller mean. A random sample of measurement of inspection time taken after the new method had become established gave the following distribution:   Time (sec) 120 129 135 144 157 173 179 191 Number 1 3 2 3 4 3 3 4   Your manager thinks that the introduction of the new method of inspection has been very                                          effective in reducing the inspection time. Using the data provided and assuming the inspection time to be normally distributed with a standard deviation of 28 seconds, test this hypothesis at 5% level of significance

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
Section: Chapter Questions
Problem 25SGR
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The mean inspection time, using the current method of quality control, has been found over a long period of time to be 160 seconds. Your manager decides to introduce a new method of quality control aimed at reducing this to as short as possible and so she expects the new method to produce a smaller mean. A random sample of measurement of inspection time taken after the new method had become established gave the following distribution:

 

Time (sec)

120

129

135

144

157

173

179

191

Number

1

3

2

3

4

3

3

4

 

Your manager thinks that the introduction of the new method of inspection has been very                                          effective in reducing the inspection time. Using the data provided and assuming the inspection time to be normally distributed with a standard deviation of 28 seconds, test this hypothesis at 5% level of significance

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Follow-up Question

Can you explain how the highlighted boxes in the attached image a little better?

The T table i have, which is also attached( given the degree of freedom is 22)  gives a value of 1.717? 

Whereas you have given values of -1.64. Then a P value of 0.432? Can you explain further how you have reached these different figures?

2 x - l S/√n = At 5% level of significance. α = 0.05 Critical value LLAR = = & P-value 159 - 160 28 P -0.1713 20.05 =-1.64 2 <0·1213] 0.432 $ Obtained from 2-table lor Normal probability calculator 4 Since. 2 > 2x and P-value > α, hence We accept to at 5% level of significance. |1t μ = 160. Conclude that, new method of inspection is not
Transcribed Image Text:2 x - l S/√n = At 5% level of significance. α = 0.05 Critical value LLAR = = & P-value 159 - 160 28 P -0.1713 20.05 =-1.64 2 <0·1213] 0.432 $ Obtained from 2-table lor Normal probability calculator 4 Since. 2 > 2x and P-value > α, hence We accept to at 5% level of significance. |1t μ = 160. Conclude that, new method of inspection is not
t Table cum. prob one-tail two-tails 1.00 df 1 2 3 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1.50 0.50 27 28 0.000 1.000 0.000 0.816 1.00 1.75 0.25 0.20 0.50 0.40 0.000 0.697 0.000 0.695 0.000 0.694 0.000 0.692 1.376 1.061 1.386 0.000 0.765 0.978 1.250 0.741 0.941 1.190 0.000 0.000 0.727 0.000 0.718 0.000 0.711 0.000 0.706 0.000 0.703 0.000 0.700 0.000 0.000 0.000 0.000 0.920 0.906 1.90 0.10 0.15 0.30 0.20 1.156 1.134 1.440 0.896 1.119 1.415 0.889 1.108 1.397 0.883 1.100 1.383 0.879 1.093 1.372 1.363 1.356 0.876 0.873 0.870 0.868 1.963 3.078 1.886 1.638 2.353 1.533 2.132 1.476 2.015 1.088 1.083 1.079 1.076 1.350 1.345 0.691 0.866 1.074 0.690 0.865 1.071 0.689 0.863 1.069 0.688 0.862 1.067 1.330 0.688 0.861 1.066 1.328 0.860 1.064 0.000 0.000 0.687 1.325 0.000 0.686 0.859 1.063 1.323 0.000 0.686 0.858 1.061 1.321 0.000 0.685 0.858 1.060 1.319 0.000 0.685 0.857 1.059 1.318 0.000 0.684 0.856 1.058 1.316 0.000 0.684 0.856 1.058 1.315 0.000 0.684 0.855 1.057 1.314 1.056 1.313 0.000 0.683 0.855 0.000 0.683 0.854 29 1.055 1.311 30 1.697 0.000 0.000 0.681 1.055 1.310 1.050 1.303 1.684 40 0.683 0.854 0.851 0.848 80 0.000 0.678 0.846 60 0.000 0.679 1.296 1.671 1.045 1.043 1.292 1.664 199 1305 tas 1.375 0.05 0.025 0.01 0.005 0.001 0.10 0.05 0.02 6.314 12.71 2.920 4.303 1.341 1.337 1.333 31.82 6.965 4.541 3.747 3.365 2.571 1.943 2.447 3.143 3.707 1.895 2.365 2.998 1.860 2.306 2.896 1.833 2.262 2.821 1.812 3.182 2.776 1.796 2.201 1.782 2.179 1.771 1.729 1.725 1.721 5.208 3.499 4.785 3.355 4.501 3.250 4.297 2.228 2.764 3.169 4.144 3.106 4.025 2.718 2.681 3.055 3.930 2.160 2.650 3.012 3.852 1.761 2.145 2.624 2.977 3.787 1.753 2.131 2.602 2.947 3.733 2.583 2.921 3.686 1.746 2.120 1.740 2.110 3.646 1.734 2.567 2.898 2.878 2.539 2.861 3.579 3.610 2.528 2.845 3.552 2.518 2.831 3.527 2.508 2.819 2.500 2.807 2.101 2.552 t905 0.0005 0.01 0.002 0.001 2.093 2.086 2.080 2.074 2.069 1.717 1.714 1.711 2.064 1.708 2.060 1.706 2.056 1.703 1.701 1.699 63.66 318.31 636.62 9.925 22.327 31.599 5.841 10.215 12.924 4.604 7.173 4.032 5.893 3992 2.492 2.797 2.485 2.787 2.479 2.779 2.052 2.473 2.771 2.048 2.467 2.045 2.462 2.756 2.042 2.021 2.000 1.990 3.505 3.485 8.610 6.869 5.959 3.421 2.763 3.408 3.396 2.457 2.750 3.385 2.423 2.704 3.307 2.390 2.660 3.232 2.374 2.639 3.195 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.792 3.768 3.467 3.745 3.450 3.725 3.435 3.883 3.850 3.819 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416
Transcribed Image Text:t Table cum. prob one-tail two-tails 1.00 df 1 2 3 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1.50 0.50 27 28 0.000 1.000 0.000 0.816 1.00 1.75 0.25 0.20 0.50 0.40 0.000 0.697 0.000 0.695 0.000 0.694 0.000 0.692 1.376 1.061 1.386 0.000 0.765 0.978 1.250 0.741 0.941 1.190 0.000 0.000 0.727 0.000 0.718 0.000 0.711 0.000 0.706 0.000 0.703 0.000 0.700 0.000 0.000 0.000 0.000 0.920 0.906 1.90 0.10 0.15 0.30 0.20 1.156 1.134 1.440 0.896 1.119 1.415 0.889 1.108 1.397 0.883 1.100 1.383 0.879 1.093 1.372 1.363 1.356 0.876 0.873 0.870 0.868 1.963 3.078 1.886 1.638 2.353 1.533 2.132 1.476 2.015 1.088 1.083 1.079 1.076 1.350 1.345 0.691 0.866 1.074 0.690 0.865 1.071 0.689 0.863 1.069 0.688 0.862 1.067 1.330 0.688 0.861 1.066 1.328 0.860 1.064 0.000 0.000 0.687 1.325 0.000 0.686 0.859 1.063 1.323 0.000 0.686 0.858 1.061 1.321 0.000 0.685 0.858 1.060 1.319 0.000 0.685 0.857 1.059 1.318 0.000 0.684 0.856 1.058 1.316 0.000 0.684 0.856 1.058 1.315 0.000 0.684 0.855 1.057 1.314 1.056 1.313 0.000 0.683 0.855 0.000 0.683 0.854 29 1.055 1.311 30 1.697 0.000 0.000 0.681 1.055 1.310 1.050 1.303 1.684 40 0.683 0.854 0.851 0.848 80 0.000 0.678 0.846 60 0.000 0.679 1.296 1.671 1.045 1.043 1.292 1.664 199 1305 tas 1.375 0.05 0.025 0.01 0.005 0.001 0.10 0.05 0.02 6.314 12.71 2.920 4.303 1.341 1.337 1.333 31.82 6.965 4.541 3.747 3.365 2.571 1.943 2.447 3.143 3.707 1.895 2.365 2.998 1.860 2.306 2.896 1.833 2.262 2.821 1.812 3.182 2.776 1.796 2.201 1.782 2.179 1.771 1.729 1.725 1.721 5.208 3.499 4.785 3.355 4.501 3.250 4.297 2.228 2.764 3.169 4.144 3.106 4.025 2.718 2.681 3.055 3.930 2.160 2.650 3.012 3.852 1.761 2.145 2.624 2.977 3.787 1.753 2.131 2.602 2.947 3.733 2.583 2.921 3.686 1.746 2.120 1.740 2.110 3.646 1.734 2.567 2.898 2.878 2.539 2.861 3.579 3.610 2.528 2.845 3.552 2.518 2.831 3.527 2.508 2.819 2.500 2.807 2.101 2.552 t905 0.0005 0.01 0.002 0.001 2.093 2.086 2.080 2.074 2.069 1.717 1.714 1.711 2.064 1.708 2.060 1.706 2.056 1.703 1.701 1.699 63.66 318.31 636.62 9.925 22.327 31.599 5.841 10.215 12.924 4.604 7.173 4.032 5.893 3992 2.492 2.797 2.485 2.787 2.479 2.779 2.052 2.473 2.771 2.048 2.467 2.045 2.462 2.756 2.042 2.021 2.000 1.990 3.505 3.485 8.610 6.869 5.959 3.421 2.763 3.408 3.396 2.457 2.750 3.385 2.423 2.704 3.307 2.390 2.660 3.232 2.374 2.639 3.195 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.792 3.768 3.467 3.745 3.450 3.725 3.435 3.883 3.850 3.819 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416
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