An SRS of 350 high school seniors gained an average of x¯=24 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=48.You can find the critical values to three decimal places by using the last row in table C.(a) Find a 99% confidence interval for the mean change in score μ in the population of all high school seniors. (Enter your answers rounded to two decimal places.) lower bound of confidence interval= upper bound of confidence interval= (b) What is the margin of error for 99% ? (Enter your answer rounded to two decimal places.) margin of error= (c) Suppose we had an SRS of just 100 high school seniors. What would be the margin of error for 99% confidence? (Enter your answer rounded to three decimal places.) margin of error= (d) How does decreasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same? A) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation also decrease. B) Decreasing the sample size keeps the margin of error the same, provided the confidence level and population standard deviation remain the same. C) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same. D) Decreasing the sample size decreases the margin of error, provided the confidence level and population standard deviation remain the same. TABLES699Table entry for C is the critical valuet* required for confidence level C.To approximate one- and two-sidedP-values, compare the value of the tTail areastatistic with the critical values of t*Area Cthat match the P-values given at thebottom of the table.t*TABLE C t distribution critical valuesConfidence level CDegrees offreedom50%60%70%80%90%95%96%98%99%99.5%99.8%99.9%11.0001.3761.9633.0786.31412.7115.8931.8263.66127.3318.3636.60.8161.0611.3861.8862.9204.3034.8496.9659.92514.0922.3331.601.2507.4535.59830.7650.9781.6382.3533.1823.4824.5415.84110.2112.9240.7410.9411.1901.5332.1322.7762.9993.7474.6047.1738.6100.7270.9201.1561.4762.0152.5712.7573.3654.0324.7735.8936.8696.0.7180.9061.1341.4401.9432.4472.6123.1433.7075.2084.3174.0295.95970.7110.8961.1191.4151.8952.3652.5172.9983.4994.7855.40880.7060.8891.1081.3971.8602.3062.4492.8963.3553.8334.5015.0419.0.7030.8831.1001.3831.8332.2622.3982.8213.2503.6904.2974.781100.7000.8791.0931.3721.8122.2282.3592.7643.1693.5814.1444.587110.6970.8761.0881.3631.7962.2012.3282.7183.1063.4974.0254.437120.6950.8731.0831.3561.7822.1792.3032.6813.0553.4283.9304.318130.6940.8701.0791.3501.7712.1602.2822.6503.0123.3723.8524.221140.6920.8681.0761.3451.7612.1452.2642.6242.9773.3263.7874.140150.6910.8661.0741.3411.7532.1312.2492.6022.9473.2863.7334.073160.6900.8651.0711.3371.7462.1202.2352.5832.9213.2523.6864.015170.6890.8631.0691.3331.7402.1102.2242.5672.8983.2223.6463.965180.6880.8621.0671.3301.7342.1012.2142.5522.8783.1973.6113.9221.0661.0641.7291.725190.6880.8611.3282.0932.2052.5392.8613.1743.5793.883200.6870.8601.3252.0862.1972.5282.8453.1533.5523.8501.0631.3233.1353.5273.505210.6860.8591.7212.0802.1892.5182.8313.8190.8580.858220.6861.0611.3211.7172.0742.1832.5082.8193.1193.792230.6851.0601.3193.4851.7141.7112.0692.1772.5002.8073.1043.768240.6850.8571.0591.3182.0642.1722.4922.7973.0913.4673.745250.6840.8561.0581.3161.7082.0602.1672.4852.7873.0783.4503.725260.6840.8561.0581.3151.7062.0562.1622.4792.7793.0673.4353.707270.6840.8551.0571.3141.7032.0522.1582.4732.7713.0573.4213.690280.6830.8551.0561.3131.7012.0482.1542.4672.7633.0473.4083.674290.6830.8541.0551.3111.6992.0452.1502.4622.7563.0383.3963.659300.6830.8541.0551.3101.6972.0422.1472.4572.7503.0303.3853.646400.6810.8511.0501.3031.6842.0212.1232.4232.7042.9713.3073.5510.6790.679500.8491.0471.2991.6762.0092.1092.4032.6782.9373.2613.496600.8481.0451.2961.6712.0002.0992.3902.6602.9153.2323.460800.6780.8461.0431.2921.6641.9902.0882.3742.6392.8873.1953.4161000.6770.8451.0421.2901.6601.9842.0812.3642.6262.8713.1743.39010000.6750.8421.0371.2821.6461.9622.0562.3302.5812.8133.0983.3000.6740.8411.0361.2821.6451.9602.0542.3262.5762.8073.0913.291One-sided P.25.20.15.10.05.025.02.01.005.0025.001.0005Two-sided P.50.40.30.20.10.05.04.02.01.005.002.001

(a). From this given information, the value of mean is 24, standard deviation 48 and sample size (n)…

An SRS of 350 high school seniors gained an average of x¯=24 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=48. You can find the critical values to three decimal places by using the last row in table C. (a) Find a 99% confidence interval for the mean change in score μ in the population of all high school seniors. (Enter your answers rounded to two decimal places.) lower bound of confidence interval= upper bound of confidence interval= (b) What is the margin of error for 99% ? (Enter your answer rounded to two decimal places.) margin of error= (c) Suppose we had an SRS of just 100 high school seniors. What would be the margin of error for 99% confidence? (Enter your answer rounded to three decimal places.) margin of error= (d) How does decreasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same? A) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation also decrease. B) Decreasing the sample size keeps the margin of error the same, provided the confidence level and population standard deviation remain the same. C) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same. D) Decreasing the sample size decreases the margin of error, provided the confidence level and population standard deviation remain the same

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

An SRS of 350 high school seniors gained an average of x¯=24 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ=48.

You can find the critical values to three decimal places by using the last row in table C.

(a) Find a 99% confidence interval for the mean change in score μ in the population of all high school seniors. (Enter your answers rounded to two decimal places.)

lower bound of confidence interval=

upper bound of confidence interval=

(b) What is the margin of error for 99% ? (Enter your answer rounded to two decimal places.)

margin of error=

(c) Suppose we had an SRS of just 100 high school seniors. What would be the margin of error for 99% confidence? (Enter your answer rounded to three decimal places.)

margin of error=

(d) How does decreasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same?

A) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation also decrease.

B) Decreasing the sample size keeps the margin of error the same, provided the confidence level and population standard deviation remain the same.

C) Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

D) Decreasing the sample size decreases the margin of error, provided the confidence level and population standard deviation remain the same.

TABLES
699
Table entry for C is the critical value
t* required for confidence level C.
To approximate one- and two-sided
P-values, compare the value of the t
Tail area
statistic with the critical values of t*
Area C
that match the P-values given at the
bottom of the table.
t*
TABLE C t distribution critical values
Confidence level C
Degrees of
freedom
50%
60%
70%
80%
90%
95%
96%
98%
99%
99.5%
99.8%
99.9%
1
1.000
1.376
1.963
3.078
6.314
12.71
15.89
31.82
63.66
127.3
318.3
636.6
0.816
1.061
1.386
1.886
2.920
4.303
4.849
6.965
9.925
14.09
22.33
31.60
1.250
7.453
5.598
3
0.765
0.978
1.638
2.353
3.182
3.482
4.541
5.841
10.21
12.92
4
0.741
0.941
1.190
1.533
2.132
2.776
2.999
3.747
4.604
7.173
8.610
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
5.208
4.317
4.029
5.959
7
0.711
0.896
1.119
1.415
1.895
2.365
2.517
2.998
3.499
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
1.066
1.064
1.729
1.725
19
0.688
0.861
1.328
2.093
2.205
2.539
2.861
3.174
3.579
3.883
20
0.687
0.860
1.325
2.086
2.197
2.528
2.845
3.153
3.552
3.850
1.063
1.323
3.135
3.527
3.505
21
0.686
0.859
1.721
2.080
2.189
2.518
2.831
3.819
0.858
0.858
22
0.686
1.061
1.321
1.717
2.074
2.183
2.508
2.819
3.119
3.792
23
0.685
1.060
1.319
3.485
1.714
1.711
2.069
2.177
2.500
2.807
3.104
3.768
24
0.685
0.857
1.059
1.318
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
0.679
0.679
50
0.849
1.047
1.299
1.676
2.009
2.109
2.403
2.678
2.937
3.261
3.496
60
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
0.674
0.841
1.036
1.282
1.645
1.960
2.054
2.326
2.576
2.807
3.091
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
.0005
Two-sided P
.50
.40
.30
.20
.10
.05
.04
.02
.01
.005
.002
.001

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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