A college professor teaching statistics conducts a study of 1/ randomly selected students, comparing the number of homework exercises the students completed and their scores on the final exam, claiming that the more exercises a student completes, the higher their mark will be on the exam. The study yields a sample correlation coefficient of r = 0.607. Test the professor's claim at a 1% significance level.
A college professor teaching statistics conducts a study of 1/ randomly selected students, comparing the number of homework exercises the students completed and their scores on the final exam, claiming that the more exercises a student completes, the higher their mark will be on the exam. The study yields a sample correlation coefficient of r = 0.607. Test the professor's claim at a 1% significance level.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Transcribed Image Text:A college professor teaching statistics conducts a study of 1/ randomly selected
students, comparing the number of homework exercises the students completed and
their scores on the final exam, claiming that the more exercises a student completes,
the higher their mark will be on the exam. The study yields a sample correlation
coefficient of r = 0.607. Test the professor's claim at a 1% significance level.
highlighted value
ws the critical t-value at
95% confidence level
ails 0.05,
-0.025) for a sample
h 50 degrees of freedom.
df
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150
200
MA
80% confidence
2tails=0.20
1 tail=0.10
3.078
1.886
1638
1.533
1476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1,330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.306
1.303
1.301
1.299
1.296
1.291
1292
1.291
1.290
1.289
1.287
286
90% confidence
2tails-0.10
1 tal-0.05
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1699
1.697
1.690
1.684
1.679
1.676
1.671
1.667
1.664
1662
1.660
1.658
1655
1652
95% confidence 98% confidence 99% confidence
2 taills=0.02
1 tall=0.01
2tails=0.06
1 taill=0.025
12.706
4.303
3.182
2.776
2571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.030
2.021
2014
2009
2.000
1.994
1.990
1.987
1.984
1,950
1.976
1972
31.820
6.965
4.541
3.747
3.365
3.143
2.998
2.897
2.821
2764
2.718
2.681
2.650
2.625
2.602
2.584
2.567
2.552
2.539
2528
2518
2508
2.500
2.492
2485
2.479
2.473
2.467
2462
2.457
2.438
2.423
2412
2.403
2390
2.381
2.374
2.369
2361
2.358
2.351
2345
2tails=0.01
1 taill=0.005
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.724
2.701
2.690
2678
2660
2,648
2639
2632
2626
2617
2.609
Transcribed Image Text:a. Calculate the test statistic.
t
Round to three decimal places if necessary
b. Determine the critical value(s) for the hypothesis test.
Round to three decimal places if necessary
c. Conclude whether to reject the null hypothesis or not based on the test statistic.
O Reject
O Fail to Reject
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