i sample data Community College Transfer No Transfer 274 1190 Sample mean time to graduate, in years Sample standard 5.45 4.53 1.142 1.002 deviation time to graduate, in years Print Done
i sample data Community College Transfer No Transfer 274 1190 Sample mean time to graduate, in years Sample standard 5.45 4.53 1.142 1.002 deviation time to graduate, in years Print Done
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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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
Transcribed Image Text:A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain year, monitoring the progress the students made toward completing a bachelor's degree. One aspect of his research was to
determine whether students who first attended community college took longer to attain a bachelor's degree than those who immediately attended and remained at a 4-year institution. The data in the table attached below summarize the results of
his study. Complete parts a) through e) below.
Click here to view the sample data.
Click here to view Student's t-distribution table.
A. The response variable is the time to graduate. The explanatory variable is the use of community college or not.
B. The response variable is the use of community college or not. The explanatory variable is the time to graduate.
C. The response variable is the time to graduate. The explanatory variable is the number of students.
D. The response variable is the number of students. The explanatory variable is the time to graduate.
b) Explain why this study can be analyzed using inference of two sample means. Select all that apply.
A. The sample sizes are large (both greater than or equal to 30).
B. The population is given to be normally distributed.
C. The samples can be reasonably assumed to be random.
D.
The sample sizes are not more than 5% of the population.
E. The samples are independent.
c) Does the evidence suggest that community college transfer students take longer to attain a bachelor's degree? Use an a= 0.10 level of significance. Perform a hypothesis test. Determine the null and alternative hypotheses.
O A. Ho: Pcommunity college Hno transfer: H1: Pcommunity college
> Hno transfer
B. Ho: Hcommunity college = Pno transfer: H1: Hcommunity college Hno transfer
C. Ho: Pcommunity college = Hno transfer: H1: Hcommunity college > Hno transfer
D. Ho: Hcommunity college > Hno transfer: H1: Pcommunity college Hno transfer
Determine the test statistic.
t =
| (Round to two decimal places as needed.)
Transcribed Image Text:Area in
right tail
t-Distribution
Area in Right Tail
Degrees of
Freedom
0.25
0.20
0.15
0.10
0.05 0.025
0.02
0.01
0.005
0.0025
0.001
0.0005
sample data
3.078
1.886
1.638
1.533
1.476
63.657
1.000
0.816
0.765
0.741
0.727
1.376
1.061
0.978
1.963
1.386
1.250
6.314
2.920
2.353
2.132
2.015
12.706
4.303
3.182
2.776
2.571
15.894
4.849
3.482
2.999
2.757
127.321
14.089
7.453
5.598
4.773
31.821
6.965
318.309
22.327
4.541
3.747
3.365
9.925
5.841
4.604
4.032
10.215
7173
5.893
636.619
31.599
12.924
8.610
6.869
0.941
0.920
1.190
1.156
Community
College Transfer
274
No Transfer
1.943
1.895
1.860
1.833
1.812
0.906
1.440
1.415
1.397
1.383
1.372
2.612
2.517
2.449
2.398
2.359
3.707
0.718
0.711
0.706
0.703
0.700
1.134
1.119
1.108
1.100
1.093
2.447
2.365
2.306
2.262
2.228
3.143
2.998
2.896
2.821
2.764
4.317
4.029
3.833
3.690
3.581
5.208
4.785
4.501
4.297
4.144
5.959
5.408
5.041
4.781
4.587
7
8
0.896
0.889
0.883
0.879
3.499
3.355
3.250
3.169
1190
Sample mean time to
graduate, in years
Sample standard
deviation time to
10
5.45
4.53
0.697
0.695
0.876
1.088
1.363
1.356
1.350
1.345
1.341
1.796
2.201
2.179
2.160
2.145
2.131
2.328
2.303
2.282
2.264
2.249
3.497
3.428
11
12
13
14
15
0.873
0.870
0.868
0.866
1.083
1.079
1.076
1.074
1.782
1.771
1.761
1.753
2.718
2.681
2.650
2.624
2.602
3.106
3.055
3.012
2.977
2.947
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
1.142
1.002
0.694
0.692
0.691
3.372
3.326
3.286
4.140
4.073
graduate, in years
16
17
18
19
20
0.690
0.689
0.688
0.865
0,863
0.862
0.861
0.860
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
2.861
2.845
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
1.071
1.069
1.067
1.066
1.064
1.337
1.333
1.330
1.328
1.325
1.746
1.740
1.734
1.729
1.725
0.688
0.687
Print
Done
0.686
0.686
0.685
0.685
0.684
1.323
1.321
1.319
1.318
1.316
2.080
2.074
2.069
2.064
2.060
3.527
3.505
3.485
3.467
3.450
3.819
3.792
3.768
3.745
3.725
1.063
1.061
1.721
1.717
21
22
23
24
25
0.859
0.858
0.858
0.857
1.060
1.059
1.058
1.714
1.711
1.708
2.189
2.183
2.177
2.172
2.167
2.518
2.508
2.500
2.492
2.485
2.831
2.819
2.807
2.797
2.787
3.135
3.119
3.104
3.091
0.856
3.078
26
27
28
29
0.684
0.684
0.683
0.683
0.856
0.855
0.855
0.854
1.058
1.057
1.056
1.055
1.315
1.314
1.313
1.311
1.706
1.703
1.701
1.699
2.056
2.052
2.048
2.045
2.162
2.158
2.154
2.150
2.479
2.473
2.467
2.462
2.779
2.771
2.763
2.756
3.067
3.057
3.047
3.038
3.435
3.421
3.408
3.396
3.707
3.690
3.674
3.659
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