A sample of 49 observations is taken from a normal population with a population standard deviation of 10. The sample mean is 55. (use z Distribution Table) Determine the 99% confidence interval for the population mean. Round your answets to 2 decimal places What is the Confindence interval for the population mean is and
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The margin of error is given by the formula: Margin of Error = z * (population standard deviation / sqrt(sample size)) Given that the confidence level is 99%, we need to find the z-value corresponding to this confidence level. From the z Distribution Table, the Show more…
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(9) Construct and interpret a Confidence Interval to estimate an entire population’s Mean Grade point averages for 10 randomly selected college students are listed below. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 Assume grade point averages are normally distributed (that is, have a Normal/Bell-shaped distribution). (a) Find a point estimate x̄ for the population mean. (b) Find the Margin of Error for a 98% confidence interval. You must use the correct critical value from Table VII. (c) Construct a 98% confidence interval for the population mean. (d) Interpret the confidence interval, “We are 98% confident that ….” Table VII t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.657 127.321 318.309 636.619 2 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 3 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.215 12.924 4 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 5 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 6 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 7 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 8 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 19 0.688 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 21 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 22 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 23 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768
Adi S.
A 95 % confidence interval for the population standard deviation is given by ( ) 50.74 39.08 20.17 81.57 57.17 77.74 76.27 42.66 82.06 77.57 87.11 56.48 68.57 63.45 66.79 48.34 26.29 25.05 51.04 48.4 54.54 64.02 43.43 56.19 64.92 99.31 59.78 47.05 42.18 63.33 45.84 89.07 51.57 80.92 39.1 51.19 70.17 59.31 76.17 40.5 57.56 59.42 74.11 89.14 51.17 39.33 70.91 70.89 64.26 67.68 37.09 57.62 61.69 50.74 55.4 90.77 50.66 100.91 57.28 37.32 38.7 52.86 56.39 29.65 78.7 53.45 41.47 38.23 61.15 99.24 74.87 52.02 63.1 44.76 31.55 76.4 16.04 28.42 67.92 60.71 56.55 82.69 70.31 57.16 24.28 69.77 54.48 75.25 64.05 24.49 39 72.32 70.22 35.77 61.17 51.32 64.76 105.23 66.13 19.99
Lucas F.
The purpose of a confidence interval is to ________. For an independent-measures research study, the value of Cohen's d or r² helps to describe ________. 19. A researcher reports t(24) = 5.30 for an independent-measures experiment. How many individuals participated in the entire experiment? 20. Each student at a school has a student identification number. Counselors have a computer generate 50 random identification numbers and those students are asked to take a survey. What type of sampling is this? 21. A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one tailed hypothesis test, and the test produces z = -1.85. Based on this result, what is the correct statistical decision? 22. When a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. On average, the size of the difference between the sample mean and the population mean is predicted by ________. 23. In what circumstances is the t statistic used instead of a z-score for a hypothesis test?
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