A simple random sample of size n is drawn. The sample mean, x , is found to be 19.1 and the sample standard deviation, s, is found to be 4.5
(a) Construct a 95% confidence interval about mu if the sample size, n, is 35.
Lower bound: ________;
Upper bound: _________
(b) Construct a 95% confidence interval about muμ
if the sample size, n, is 51.
Lower bound: ______;
Upper bound: _____
(Use ascending order. Round to two decimal places as needed.)
How does increasing the sample size affect the margin of error, E?
A. The margin of error decreases.
B. The margin of error increases.
C. The margin of error does not change.
(c) Construct a 99% confidence interval about mu if the sample size, n, is 35.
Lower bound: ______;
Upper bound: ______
(Use ascending order. Round to two decimal places as needed.)
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?
A. The margin of error decreases.
B. The margin of error does not change.
C. The margin of error increases.
(d) If the sample size is 13,
what conditions must be satisfied to compute the confidence interval?
A. The sample must come from a population that is normally distributed and the sample size must be large.
B. The sample size must be large and the sample should not have any outliers.
C. The sample data must come from a population that is normally distributed with no outliers.
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 3.611 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
24 0.685 0.857
1.059 1.318 1.711
2.064 2.172 2.492
2.797 3.091 3.467 3.745
25 0.684 0.856
1.058 1.316 1.708
2.060 2.167 2.485
2.787 3.078 3.450 3.725
26 0.684 0.856
1.058 1.315 1.706
2.056 2.162 2.479
2.779 3.067 3.435 3.707
27 0.684 0.855
1.057 1.314 1.703
2.052 2.158 2.473
2.771 3.057 3.421 3.690
28 0.683 0.855
1.056 1.313 1.701
2.048 2.154 2.467
2.763 3.047 3.408 3.674
29 0.683 0.854
1.055 1.311 1.699
2.045 2.150 2.462
2.756 3.038 3.396 3.659
30 0.683 0.854
1.055 1.310 1.697
2.042 2.147 2.457
2.750 3.030 3.385 3.646
40 0.681 0.851
1.050 1.303 1.684
2.021 2.123 2.423
2.704 2.971 3.307 3.551
50 0.679 0.849
1.047 1.299 1.676
2.009 2.109 2.403
2.678 2.937 3.261 3.496
60 0.679 0.848
1.045 1.296 1.671
2.000 2.099 2.390
2.660 2.915 3.232 3.460
80 0.678 0.846
1.043 1.292 1.664
1.990 2.088 2.374
2.639 2.887 3.195 3.416
100 0.677 0.845
1.042 1.290 1.660
1.984 2.081 2.364
2.626 2.871 3.174 3.390
1000 0.675 0.842
1.037 1.282 1.646
1.962 2.056 2.330
2.581 2.813 3.098 3.300
z 0.674 0.841 1.036
1.282 1.645 1.960
2.054 2.326 2.576
2.807 3.091 3.291
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
a)
| sample mean 'x̄= | 19.10 |
| sample size n= | 35.00 |
| sample std deviation s= | 4.50 |
| std error 'sx=s/√n= | 0.7606 |
| for 95% CI; and 34 df, value of t= | 2.032 | |
| margin of error E=t*std error = | 1.546 | |
| lower bound=sample mean-E = | 17.55 | |
| Upper bound=sample mean+E = | 20.65 | |
b)
| for 95% CI; and 50 df, value of t= | 2.009 | |
| margin of error E=t*std error = | 1.266 | |
| lower bound=sample mean-E = | 17.83 | |
| Upper bound=sample mean+E = | 20.37 | |
A. The margin of error decreases.
c)
| for 99% CI; and 34 df, value of t= | 2.728 | |
| margin of error E=t*std error = | 2.075 | |
| lower bound=sample mean-E = | 17.02 | |
| Upper bound=sample mean+E = | 21.18 | |
C. The margin of error increases.
d)
C. The sample data must come from a population that is normally distributed with no outliers.
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