Answer the following questions referring to the MINITAB simulation of confidence intervals given in the photo below" In theory, how many of the intervals would you expect to contain the true population mean U ( = 10)? How many of the intervals actually contain the mean of the population? If this simulation were repeated would you always find that the same number of intervals contain U?

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Question 2: Answer the following questions referring to the MINITAB simulation of confidence intervals given in the photo below"

  • In theory, how many of the intervals would you expect to contain the true population mean U ( = 10)?
  • How many of the intervals actually contain the mean of the population?
  • If this simulation were repeated would you always find that the same number of intervals contain U?
MTB
random 25 c1-c40;
The first two commands on the left select 40 random samples
each of size n = 25, from a Normal distribution with u = 10,
SUBC> norm 10 1.5.
and o= 1.5.
МТВ
zint 95 1.5 c1-c40
The third command forms the 95% Z-interval for each sample
Confidence Intervals
The assumed sigma
1.50
Variable
n
Mean
St Dev
SE Mean
95.0 % C.I.
10.698)
10.980)
9.522,
9.804,
9.502,
9.046,
8.830,
C1
10.110
1.091
0.300
C2
25
10.392
1.658
0.300
10.679)
10.222)
10.007)
25
10.091
1.323
0.300
25
9.634
1.373
0.300
25
9.418
1.700
0.300
25
10.936
1.562
0.300
10.348,
11.524) x
10.429
0.300
11.017)
10.377)
10.356)
25
1.200
9.841,
9.200,
9.180,
9.897,
9.616,
25
9.788
1.648
0.300
25
9.768
1.744
0.300
C10
25
10.485
1.597
0.300
11.074)
C11
25
10.204
0.964
0.300
10.792)
10.284,
9.408,
9.616,
9.337,
9.162,
9.748,
8.942,
0.300
11.460) x
10.584)
10.793)
C12
25
10.872
1.338
C13
25
9.996
1.451
0.300
C14
25
10.204
1.648
0.300
C15
25
9.925
1.677
0.300
10.513)
C16
25
9.750
1.633
0.300
10.339)
C17
25
10.337
1.418
0.300
10.925)
C18
25
9.530
1.336
0.300
10.118)
C19
25
9.331
1.304
0.300
8.743,
9.565,
9.202,
9.403,
9.325,
8.831,
9.443,
9.450,
9.592,
9.708,
9.259,
9.593,
9.320,
9.624,
9.492,
9.472,
9.428,
9.949,
9.491,
9.919) x
10.741)
10.378)
C20
25
10.153
1.733
0.300
C21
25
9.790
1.582
0.300
C22
25
9.991
1.300
0.300
10.579)
C23
25
9.913
1.221
0.300
10.501)
10.007)
C24
25
9.419
1.389
0.300
C25
25
10.031
1.498
0.300
10.619)
10.627)
10.769)
10.884)
C26
25
10.039
1.531
0.300
C27
25
10.180
1.711
0.300
C28
25
10.296
1.314
0.300
C29
25
9.847
1.463
0.300
10.435)
10.182
0.300
10.770)
10.497)
C30
25
1.371
C31
9.908
1.526
0.300
C32
25
10.212
1.694
0.300
10.800)
10.669)
10.648)
10.604)
11.125)
C33
25
10.080
1.291
0.300
C34
25
10.060
1.534
0.300
C35
25
10.016
1.644
0.300
C36
25
10.537
1.401
0.300
C37
25
10.079
1.641
0.300
10.667)
10.258
1.703
0.300
10.846)
9.670,
9.254,
9.820,
C38
10.430)
10.996)
C39
25
9.842
2.250
0.300
C40
25
10.408
1.284
0.300
E LO LO LO
LO LO LO LO
N N N N N N N N N N N
Transcribed Image Text:MTB random 25 c1-c40; The first two commands on the left select 40 random samples each of size n = 25, from a Normal distribution with u = 10, SUBC> norm 10 1.5. and o= 1.5. МТВ zint 95 1.5 c1-c40 The third command forms the 95% Z-interval for each sample Confidence Intervals The assumed sigma 1.50 Variable n Mean St Dev SE Mean 95.0 % C.I. 10.698) 10.980) 9.522, 9.804, 9.502, 9.046, 8.830, C1 10.110 1.091 0.300 C2 25 10.392 1.658 0.300 10.679) 10.222) 10.007) 25 10.091 1.323 0.300 25 9.634 1.373 0.300 25 9.418 1.700 0.300 25 10.936 1.562 0.300 10.348, 11.524) x 10.429 0.300 11.017) 10.377) 10.356) 25 1.200 9.841, 9.200, 9.180, 9.897, 9.616, 25 9.788 1.648 0.300 25 9.768 1.744 0.300 C10 25 10.485 1.597 0.300 11.074) C11 25 10.204 0.964 0.300 10.792) 10.284, 9.408, 9.616, 9.337, 9.162, 9.748, 8.942, 0.300 11.460) x 10.584) 10.793) C12 25 10.872 1.338 C13 25 9.996 1.451 0.300 C14 25 10.204 1.648 0.300 C15 25 9.925 1.677 0.300 10.513) C16 25 9.750 1.633 0.300 10.339) C17 25 10.337 1.418 0.300 10.925) C18 25 9.530 1.336 0.300 10.118) C19 25 9.331 1.304 0.300 8.743, 9.565, 9.202, 9.403, 9.325, 8.831, 9.443, 9.450, 9.592, 9.708, 9.259, 9.593, 9.320, 9.624, 9.492, 9.472, 9.428, 9.949, 9.491, 9.919) x 10.741) 10.378) C20 25 10.153 1.733 0.300 C21 25 9.790 1.582 0.300 C22 25 9.991 1.300 0.300 10.579) C23 25 9.913 1.221 0.300 10.501) 10.007) C24 25 9.419 1.389 0.300 C25 25 10.031 1.498 0.300 10.619) 10.627) 10.769) 10.884) C26 25 10.039 1.531 0.300 C27 25 10.180 1.711 0.300 C28 25 10.296 1.314 0.300 C29 25 9.847 1.463 0.300 10.435) 10.182 0.300 10.770) 10.497) C30 25 1.371 C31 9.908 1.526 0.300 C32 25 10.212 1.694 0.300 10.800) 10.669) 10.648) 10.604) 11.125) C33 25 10.080 1.291 0.300 C34 25 10.060 1.534 0.300 C35 25 10.016 1.644 0.300 C36 25 10.537 1.401 0.300 C37 25 10.079 1.641 0.300 10.667) 10.258 1.703 0.300 10.846) 9.670, 9.254, 9.820, C38 10.430) 10.996) C39 25 9.842 2.250 0.300 C40 25 10.408 1.284 0.300 E LO LO LO LO LO LO LO N N N N N N N N N N N
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