Question
Asked Oct 21, 2019
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Construct a 95% confidence interval of the population proportion using the given information
x = 75, n 250
The lower bound is
The upper bound is
(Round to three decimal places as needed.)
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Construct a 95% confidence interval of the population proportion using the given information x = 75, n 250 The lower bound is The upper bound is (Round to three decimal places as needed.)

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Expert Answer

Step 1

Formula for confidence interval:

CI = Point estimate ± Margin of error.

The approximate 100*(1–α)% confidence interval for the population proportion will be obtained using the formula given below:

P1-pp/
P(1-p)
spsp+z
СI
п
п
Here, p be the sample proporti on, n is sample size,
p is population proporti on and
Z
two tailed critical value of standard normal
di stribution
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P1-pp/ P(1-p) spsp+z СI п п Here, p be the sample proporti on, n is sample size, p is population proporti on and Z two tailed critical value of standard normal di stribution

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Step 2

Sample proportion can be calculated as  shown below.

75
= 0.3
250
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75 = 0.3 250

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Step 3

Z value can be calculate...

a 0.05
a/2 0.025
1 -a/2 0.975
4-a/2 =1.96
00
.01
.02
.03
.04
.05
.06
07
.08
09
5319
5080
5120
5160
5199
5239
5279
5359
0.0
5000
5040
5517
5714
5753
0.1
.5398
5438
5478
5557
.5596
.5636
5675
5793
5832
5871
5910
.5948
.5987
6026
.6064
6103
.6141
0.2
6443
6480
.6517
0.3
6179
.6217
6255
6293
.6331
6368
6736
6406
0.4 .6554
0.5
6915
0.6
6700
.6591
.6628
.6664
.6772 .6808
6844
.6879
7123
7157
7190
7224
.6950
6985
7019
7054
7088
7422
7257
7291
7324
7357
7389
7454
.7486
7517
7549
7673
7967
8238
8485
.8708
7734
.7764
.7794
8078
7823
7852
0.7
7580
7611
7642
7704
8023
0.8
7881
.7910
7939
7995
8051
8106
8133
8264
8289
8315
8340
8365
8389
0.9
8159
8186
8212
1.0
.8413
.8438
.8461
.8508
8531
.8554
.8577
8599
.8621
8686
8729
8749
8770
8790
8980
8810
8830
1.1
8643
8665
8997
.9015
1.2
.8849
.8869
8888
.8907
.8925
.8944
.8962
.9049
9066
.9082
.9099
.9115
9131
.9147
9162
.9177
1.3
.9032
.9306
.9192
.9222
.9236
9251
.9292
9319
1.4
.9207
9265
.9279
.9332
.9345
.9357
.9370
9382
.9394
.9406
9418
.9429
.9441
1.5
.9525
.9535
.9545
.9452
.9463
.9495
.9505 .9515
1.6
9474
.9484
1.7
.9554
.9564
9573
.9582
9591
.9599
9608
9616
.9625
9633
.9678
9686
9693
.9699
9706
.9641
.9649 .9656
.9664
9671
1.8
1.9
9713
.9719
.9726
9732
9738
9744
9750
9756
9761
.9767
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a 0.05 a/2 0.025 1 -a/2 0.975 4-a/2 =1.96 00 .01 .02 .03 .04 .05 .06 07 .08 09 5319 5080 5120 5160 5199 5239 5279 5359 0.0 5000 5040 5517 5714 5753 0.1 .5398 5438 5478 5557 .5596 .5636 5675 5793 5832 5871 5910 .5948 .5987 6026 .6064 6103 .6141 0.2 6443 6480 .6517 0.3 6179 .6217 6255 6293 .6331 6368 6736 6406 0.4 .6554 0.5 6915 0.6 6700 .6591 .6628 .6664 .6772 .6808 6844 .6879 7123 7157 7190 7224 .6950 6985 7019 7054 7088 7422 7257 7291 7324 7357 7389 7454 .7486 7517 7549 7673 7967 8238 8485 .8708 7734 .7764 .7794 8078 7823 7852 0.7 7580 7611 7642 7704 8023 0.8 7881 .7910 7939 7995 8051 8106 8133 8264 8289 8315 8340 8365 8389 0.9 8159 8186 8212 1.0 .8413 .8438 .8461 .8508 8531 .8554 .8577 8599 .8621 8686 8729 8749 8770 8790 8980 8810 8830 1.1 8643 8665 8997 .9015 1.2 .8849 .8869 8888 .8907 .8925 .8944 .8962 .9049 9066 .9082 .9099 .9115 9131 .9147 9162 .9177 1.3 .9032 .9306 .9192 .9222 .9236 9251 .9292 9319 1.4 .9207 9265 .9279 .9332 .9345 .9357 .9370 9382 .9394 .9406 9418 .9429 .9441 1.5 .9525 .9535 .9545 .9452 .9463 .9495 .9505 .9515 1.6 9474 .9484 1.7 .9554 .9564 9573 .9582 9591 .9599 9608 9616 .9625 9633 .9678 9686 9693 .9699 9706 .9641 .9649 .9656 .9664 9671 1.8 1.9 9713 .9719 .9726 9732 9738 9744 9750 9756 9761 .9767

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