Use MINTAB to construct a 85% confidence interval for the population mean. { Sta
ID: 3066698 • Letter: U
Question
Use MINTAB to construct a 85% confidence interval for the population mean. { Stat/Basic Statistics/1-sample t} 2.) In MINITAB generate 100 columns of data with 100 observations in each column from a Normal distribution with ?-46 and ?_5 Calc Random DatalNormal }. Find an appropriate 92% confidence interval for the population mean using each of the 100 samples. { Stat/Basic Statistics/1-sample z ) a.)What are the 100 confidence intervals (MINTAB output)? b.)How many of these intervals are expected to contain the mean of the population? Based on your Minitab output, how many of these intervals actually contain the mean of the population (1-46)? c.)Explanation / Answer
Code and Output of MINITAB
MTB > OneZ C1-C100;
SUBC> Sigma 5;
SUBC> Test 46;
SUBC> Confidence 92.
One-Sample Z: C1, C2, C3, C4, C5, C6, C7, C8, ...
Test of mu = 46 vs not = 46
The assumed standard deviation = 5
Variable N Mean StDev SE Mean 92% CI Z P
C1 100 46.758 4.448 0.500 (45.883, 47.634) 1.52 0.129
C2 100 46.205 5.029 0.500 (45.330, 47.081) 0.41 0.681
C3 100 46.514 5.616 0.500 (45.638, 47.389) 1.03 0.304
C4 100 46.130 5.243 0.500 (45.255, 47.006) 0.26 0.794
C5 100 45.995 4.849 0.500 (45.119, 46.870) -0.01 0.991
C6 100 45.523 5.198 0.500 (44.648, 46.399) -0.95 0.340
C7 100 46.775 5.034 0.500 (45.900, 47.651) 1.55 0.121
C8 100 46.364 4.228 0.500 (45.489, 47.239) 0.73 0.467
C9 100 46.326 4.703 0.500 (45.451, 47.201) 0.65 0.514
C10 100 44.870 4.920 0.500 (43.994, 45.745) -2.26 0.024
C11 100 45.797 5.406 0.500 (44.922, 46.673) -0.41 0.685
C12 100 45.339 4.873 0.500 (44.464, 46.215) -1.32 0.186
C13 100 45.830 5.020 0.500 (44.955, 46.706) -0.34 0.734
C14 100 46.597 4.865 0.500 (45.722, 47.472) 1.19 0.232
C15 100 46.690 4.951 0.500 (45.814, 47.565) 1.38 0.168
C16 100 46.941 4.929 0.500 (46.066, 47.817) 1.88 0.060
C17 100 45.842 5.326 0.500 (44.967, 46.717) -0.32 0.752
C18 100 46.098 5.974 0.500 (45.223, 46.973) 0.20 0.844
C19 100 47.017 4.994 0.500 (46.142, 47.893) 2.03 0.042
C20 100 46.352 5.009 0.500 (45.476, 47.227) 0.70 0.482
C21 100 46.399 5.053 0.500 (45.524, 47.275) 0.80 0.425
C22 100 46.299 4.917 0.500 (45.424, 47.174) 0.60 0.550
C23 100 46.570 4.933 0.500 (45.694, 47.445) 1.14 0.255
C24 100 46.072 4.969 0.500 (45.196, 46.947) 0.14 0.886
C25 100 46.255 4.849 0.500 (45.380, 47.131) 0.51 0.610
C26 100 46.210 4.509 0.500 (45.334, 47.085) 0.42 0.675
C27 100 46.318 5.324 0.500 (45.442, 47.193) 0.64 0.525
C28 100 45.884 5.555 0.500 (45.009, 46.759) -0.23 0.817
C29 100 46.441 5.033 0.500 (45.565, 47.316) 0.88 0.378
C30 100 46.821 5.838 0.500 (45.945, 47.696) 1.64 0.101
C31 100 45.172 5.219 0.500 (44.297, 46.048) -1.66 0.098
C32 100 45.859 5.450 0.500 (44.984, 46.735) -0.28 0.779
C33 100 45.344 5.105 0.500 (44.469, 46.220) -1.31 0.190
C34 100 45.297 4.703 0.500 (44.422, 46.173) -1.41 0.160
C35 100 46.633 5.061 0.500 (45.758, 47.509) 1.27 0.205
C36 100 46.155 5.162 0.500 (45.279, 47.030) 0.31 0.757
C37 100 45.565 5.590 0.500 (44.689, 46.440) -0.87 0.384
C38 100 45.692 5.168 0.500 (44.817, 46.568) -0.62 0.538
C39 100 46.282 5.162 0.500 (45.407, 47.158) 0.56 0.572
C40 100 46.240 4.997 0.500 (45.365, 47.115) 0.48 0.631
C41 100 46.311 5.228 0.500 (45.436, 47.187) 0.62 0.533
C42 100 45.563 5.394 0.500 (44.688, 46.439) -0.87 0.383
C43 100 45.347 5.028 0.500 (44.471, 46.222) -1.31 0.191
C44 100 46.315 4.626 0.500 (45.440, 47.191) 0.63 0.528
C45 100 46.333 4.628 0.500 (45.457, 47.208) 0.67 0.506
C46 100 45.462 4.799 0.500 (44.586, 46.337) -1.08 0.282
C47 100 45.702 5.063 0.500 (44.827, 46.577) -0.60 0.551
C48 100 46.036 4.913 0.500 (45.160, 46.911) 0.07 0.943
C49 100 45.936 4.793 0.500 (45.061, 46.812) -0.13 0.899
C50 100 45.823 5.085 0.500 (44.948, 46.699) -0.35 0.724
C51 100 45.347 5.129 0.500 (44.471, 46.222) -1.31 0.191
C52 100 46.114 4.913 0.500 (45.239, 46.989) 0.23 0.819
C53 100 45.844 5.076 0.500 (44.968, 46.719) -0.31 0.755
C54 100 46.059 5.072 0.500 (45.184, 46.935) 0.12 0.906
C55 100 46.943 4.426 0.500 (46.067, 47.818) 1.89 0.059
C56 100 47.007 5.086 0.500 (46.132, 47.882) 2.01 0.044
C57 100 45.233 5.461 0.500 (44.357, 46.108) -1.53 0.125
C58 100 46.156 4.838 0.500 (45.280, 47.031) 0.31 0.755
C59 100 45.567 5.338 0.500 (44.692, 46.442) -0.87 0.386
C60 100 45.538 4.904 0.500 (44.663, 46.413) -0.92 0.355
C61 100 47.198 4.173 0.500 (46.323, 48.074) 2.40 0.017
C62 100 46.354 5.096 0.500 (45.479, 47.229) 0.71 0.479
C63 100 45.830 4.893 0.500 (44.955, 46.705) -0.34 0.734
C64 100 46.203 4.904 0.500 (45.328, 47.078) 0.41 0.685
C65 100 46.035 5.028 0.500 (45.159, 46.910) 0.07 0.945
C66 100 46.307 4.609 0.500 (45.431, 47.182) 0.61 0.540
C67 100 46.448 5.636 0.500 (45.572, 47.323) 0.90 0.371
C68 100 45.372 5.061 0.500 (44.497, 46.248) -1.26 0.209
C69 100 46.677 4.909 0.500 (45.802, 47.552) 1.35 0.176
C70 100 45.948 4.811 0.500 (45.072, 46.823) -0.10 0.916
C71 100 45.350 5.180 0.500 (44.475, 46.225) -1.30 0.194
C72 100 46.010 5.398 0.500 (45.135, 46.886) 0.02 0.983
C73 100 46.491 4.816 0.500 (45.616, 47.367) 0.98 0.326
C74 100 45.579 5.083 0.500 (44.703, 46.454) -0.84 0.399
C75 100 45.047 4.822 0.500 (44.172, 45.923) -1.91 0.057
C76 100 47.021 4.942 0.500 (46.146, 47.897) 2.04 0.041
C77 100 46.145 5.171 0.500 (45.269, 47.020) 0.29 0.773
C78 100 45.091 4.641 0.500 (44.216, 45.967) -1.82 0.069
C79 100 45.659 4.313 0.500 (44.784, 46.534) -0.68 0.495
C80 100 45.756 5.524 0.500 (44.881, 46.632) -0.49 0.626
C81 100 45.642 4.539 0.500 (44.767, 46.518) -0.72 0.475
C82 100 46.043 5.206 0.500 (45.168, 46.919) 0.09 0.931
C83 100 45.868 5.056 0.500 (44.993, 46.744) -0.26 0.792
C84 100 45.756 5.385 0.500 (44.881, 46.632) -0.49 0.626
C85 100 45.698 4.451 0.500 (44.822, 46.573) -0.60 0.545
C86 100 45.886 4.792 0.500 (45.010, 46.761) -0.23 0.819
C87 100 46.606 5.235 0.500 (45.730, 47.481) 1.21 0.226
C88 100 46.300 5.493 0.500 (45.424, 47.175) 0.60 0.549
C89 100 45.638 5.099 0.500 (44.762, 46.513) -0.72 0.469
C90 100 45.612 4.986 0.500 (44.737, 46.487) -0.78 0.438
C91 100 45.125 5.404 0.500 (44.250, 46.000) -1.75 0.080
C92 100 46.201 4.601 0.500 (45.325, 47.076) 0.40 0.688
C93 100 46.487 5.191 0.500 (45.611, 47.362) 0.97 0.330
C94 100 45.226 4.773 0.500 (44.351, 46.102) -1.55 0.122
C95 100 46.074 4.186 0.500 (45.199, 46.949) 0.15 0.882
C96 100 46.274 4.511 0.500 (45.399, 47.149) 0.55 0.584
C97 100 46.351 4.726 0.500 (45.476, 47.226) 0.70 0.483
C98 100 45.868 4.954 0.500 (44.992, 46.743) -0.26 0.791
C99 100 46.022 4.540 0.500 (45.146, 46.897) 0.04 0.966
C100 100 45.745 4.997 0.500 (44.870, 46.621) -0.51 0.610
There are 8 such samples whose 92% confidence intervals does not included population mean. ( Mentioned in BOLD font).
There is one confidence interval whose P-value is exactly 0.08 (Corresponding to C91)
b]
we expected that there are 92 confidence intervals in that 100 groups which include the population mean.
c]
And actual there are 92 confidence intervals which contain population mean.
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