Table 5—t-Distribution
c-confidence interval
Left-tailed test
Right-tailed test
Two-tailed test
Level of confidence, c
0.80
0.90
0.95
0.98
0.99
One tail,α
0.10
0.05
0.025
0.01
0.005
d.f.
Two tails,α
0.20
0.10
0.05
0.02
0.01
1
3.078
6.314
12.706
31.821
63.657
2
1.886
2.920
4.303
6.965
9.925
3
1.638
2.353
3.182
4.541
5.841
4
1.533
2.132
2.776
3.747
4.604
5
1.476
2.015
2.571
3.365
4.032
6
1.440
1.943
2.447
3.143
3.707
7
1.415
1.895
2.365
2.998
3.499
8
1.397
1.860
2.306
2.896
3.355
9
1.383
1.833
2.262
2.821
3.250
10
1.372
1.812
2.228
2.764
3.169
11
1.363
1.796
2.201
2.718
3.106
12
1.356
1.782
2.179
2.681
3.055
13
1.350
1.771
2.160
2.650
3.012
14
1.345
1.761
2.145
2.624
2.977
15
1.341
1.753
2.131
2.602
2.947
16
1.337
1.746
2.120
2.583
2.921
17
1.333
1.740
2.110
2.567
2.898
18
1.330
1.734
2.101
2.552
2.878
19
1.328
1.729
2.093
2.539
2.861
20
1.325
1.725
2.086
2.528
2.845
21
1.323
1.721
2.080
2.518
2.831
22
1.321
1.717
2.074
2.508
2.819
23
1.319
1.714
2.069
2.500
2.807
24
1.318
1.711
2.064
2.492
2.797
25
1.316
1.708
2.060
2.485
2.787
26
1.315
1.706
2.056
2.479
2.779
27
1.314
1.703
2.052
2.473
2.771
28
1.313
1.701
2.048
2.467
2.763
29
1.311
1.699
2.045
2.462
2.756
30
1.310
1.697
2.042
2.457
2.750
31
1.309
1.696
2.040
2.453
2.744
32
1.309
1.694
2.037
2.449
2.738
33
1.308
1.692
2.035
2.445
2.733
34
1.307
1.691
2.032
2.441
2.728
35
1.306
1.690
2.030
2.438
2.724
36
1.306
1.688
2.028
2.434
2.719
37
1.305
1.687
2.026
2.431
2.715
38
1.304
1.686
2.024
2.429
2.712
39
1.304
1.685
2.023
2.426
2.708
40
1.303
1.684
2.021
2.423
2.704
45
1.301
1.679
2.014
2.412
2.690
50
1.299
1.676
2.009
2.403
2.678
60
1.296
1.671
2.000
2.390
2.660
70
1.294
1.667
1.994
2.381
2.648
80
1.292
1.664
1.990
2.374
2.639
90
1.291
1.662
1.987
2.368
2.632
100
1.290
1.660
1.984
2.364
2.626
500
1.283
1.648
1.965
2.334
2.586
1000
1.282
1.646
1.962
2.330
2.581
∞
1.282
1.645
1.960
2.326
2.576
The critical values in Table 5 were generated using Excel.
Unit VII Assignment: Hypothesis Testing for College Tuition Cost
In this assignment, you will be using inferential statistics to determine if a claim about college tuition cost is accurate.
According to the College Board’s website, the average tuition cost per year for a public four-year college (in-state cost) is $10,230.
A) Assume that you disagree with the claim. Do you think the average tuition cost is higher? Or lower?
The cost is higher.
B) Using your answer in part A, write a set of hypotheses (null hypothesis and alternative hypothesis) to represent that claim and its complement. Replace the ?s below with the appropriate inequality signs (). Highlight the hypothesis that represents your claim.
C) Gather data for tuition cost of 20 different universities. Assume the data you gather is normally distributed.How to Create your data set:
Follow the directions to fill in the table below with 20 college’s tuition costs.
· Navigate to https:
www.collegetuitioncompare.com/compare/tables
· In the drop down menus, ONLY select School Type as “Public School” and School Level as “4 year or higher.” Leave the rest of the drop down menus as is. Then select “update.”
· Scroll down to the bottom of the list and for “Number of schools to show,” select “All.”
· The list given will be in alphabetical order. You will be selecting 20 college tuition costs from this list. Do NOT just use the first 20 entries or even 20 consecutive entries. You will need to randomly select 20 entries from the entire list. Try to make sure you have a good range of tuition costs as well.
· Write the tuition cost from the first column, “Tuition & Fees / In-State” for that college in the table below.
3565
3950
7410
4029
3505
11796
2830
7439
12620
11149
3957
4900
4740
11814
8400
9536
3683
10440
12330
12445
D) Calculate the mean and standard deviation of your data set. You may use technology such as Google Sheets, Excel, or a TI-83/TI-84. Round to the nearest hundredth.
Mean _______7526.9_____ XXXXXXXXXXStandard Deviation _____3680.5___________________
E) Using a significance level , find the critical value using the following steps.
1. What are the degrees of freedom?
2. Will this be a one-tailed or two tailed test?
3. Using table 5 from the back of your textbook (page A18 in Appendix B), what is the critical value?
F) Add the critical values to the graph below and shade the rejection region.
(Special Instruction: For this part, it is recommended that you do this by hand. You can print out this page and use the image below as a template to write on or you can create a handwritten normal curve. Take a photo of your graph and replace the image below with it. If you need any technical assistance with this process, please email Waldorf’s tech support.)
G) Calculate the test statistic. Replace the ?s in the formula with the appropriate values. Round to the nearest hundredth.
H) Add the test statistic to your graph from part F, and insert the image below.
I) What is the P-value? View the video Hypothesis Testing for the Mean (Sigma Unknown) Part II to learn how to use Google Sheets to calculate the P-value of a t-test (transcript for Hypothesis Testing for the Mean (Sigma Unknown) Part II video).
J) Make a decision to reject or fail to reject the null hypothesis using either the test statistic or the P-value. Note that the same conclusion will be reached using either method.
K) Interpret the decision in the context of the original claim.
L) If you lower the level of significance to , does your decision change? Explain your reasoning.
M) Describe the type I and type II e
ors that could occur in our test by completing each of the following statements.
· A ____________ (type I, type II) e
or will occur when the actual mean of college tuition cost is ______________ (at most, at least) $10,230 but you reject the null hypothesis, .
· A ____________ (type I, type II) e
or will occur when the actual mean of college tuition cost is ______________ (less than, greater than) $10,230 but you fail to reject the null hypothesis, .