a. Develop a scatter plot for the two variables and describe what relationship, if any, exists. b. Compute the correlation coefficient for these sample data. c. Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.01 for the hypothesis test.
a. Develop a scatter plot for the two variables and describe what relationship, if any, exists. b. Compute the correlation coefficient for these sample data. c. Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.01 for the hypothesis test.
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
Make sure to do the rounding and double check the answers please.
Transcribed Image Text:A random sample of two variables, x and y, produced the observations
shown to the right.
10
11
17
10
a. Develop a scatter plot for the two variables and describe what
relationship, if any, exists.
b. Compute the correlation coefficient for these sample data.
c. Test to determine whether the population correlation coefficient is
negative. Use a significance level of 0.01 for the hypothesis test.
11
12
16
11
18
10
12
10
20
9
15
10
Click the icon to view the t-distribution table.
a. Which graph below shows a scatter plot for these data?
OA.
OB.
OC.
OD.
Ay
20-
20-
Ay
14-
14+
10-
10+
14
10
20
10
There appears to be
linear relationship between x and y.
b. What is the correlation coefficient for these sample data?
E(Round to two decimal places as needed.)
r=
c. What are the appropriate hvpotheses to test for a negative correlation coefficient?
O A. Ho: ps0
HA: p>0
О В. Но: р+0
HA p= 0
ОС. Но р<0
HA: p20
O D. Ho: p20
HA: p<0
Ο Ε. H ρ>0
HA: ps0
O F. Ho: p=0
HẠ: p+0
Calculate the t-test statistic for correlation.
= (Round to four decimal places as needed.)
Determine the critical value(s) for the rejection region for the test statistic t. Select the correct choice below and fill in the answer box to complete your choice.
(Round to four decimal places as needed.)
O A.
to.005 = +
O B. to 01 = -
O C. to.01 =
Since the test statistic
V in the rejection region,
v the null hypothesis. The data
V support the contention that the population correlation
coefficient is negative.
Transcribed Image Text:PROBABILITIES (OR AREAS UNDER 1-DISTRIBUTION CURVE)
0.3
0.95
0.025
Conf. Level
0.1
0.5
0.7
0.8
0.9
0.98
0.99 Conf. Level
0.1
0.2
One Tail
0.45
0.35
0.25
0.15
0.05
0.01
0.005 One Tail
Two Tails
0.9
0.7
0.5
0.3
0.1
0.05
0.02
0.01 Two Tails
df
Values of t
df
1
0.1584
0.5095
1.0000
1.9626
3.0777
6.3137 12.7062 31.8210 63.6559
1
0.1421
0.4447
0.8165
1.3862
1.8856
2.9200
4.3027
6.9645
9.9250
3
0.1366
0.4242
0.7649
1.2498
1.6377
2.3534
3.1824
4.5407
5.8408
3
4
0.1338
0.4142
0.7407
1.1896
1.5332
2.1318
2.7765
3.7469
4.6041
4
5
0.1322
0.4082
0.7267
1.1558
1.4759
2.0150
2.5706
3.3649
4.0321
5
6.
0.1311
0.4043
0.7176
1.1342
1.4398
1.9432
2.4469
3.1427
3.7074
7
0.1303
0.4015
0.7111
1.1192
1.4149
1,8946
2.3646
2.9979
3.4995
7
0.1297
0.3995
0.7064
1.1081
1.3968
1.8595
2.3060
2.8965
3.3554
8
9.
0.1293
0.3979
0.7027
1.0997
1.3830
1.8331
2.2622
2.8214
3.2498
9
10
0.1289
0.3966
0.6998
1.0931
1.3722
1.8125
2.2281
2.7638
3.1693
10
11
0.1286
0.3956
0.6974
1.0877
1.3634
1.7959
2.2010
2.7181
3.1058
11
12
0.1283
0.3947
0.6955
1.7823
1.0832
1.0795
1.3562
2.1788
2.6810
3.0545
12
13
0.1281
0.3940
0.6938
1.3502
1.7709
2.1604
2.6503
3.0123
13
14
0.1280
0.3933
0.6924
1.0763
1.3450
1.7613
2.1448
2.6245
2.9768
14
15
0.1278
0.3928
0.6912
1.0735
1.3406
1.7531
2.1315
2.6025
2.9467
15
16
0.1277
0.3923
0.6901
1.0711
1.3368
1.7459
2.1199
2.5835
2.9208
16
1.7396
1.7341
17
0.1276
0.3919
0.6892
1.0690
1.3334
2.1098
2.5669
2.8982
17
18
0.1274
0.3915
0.6884
1.0672
1.3304
2.1009
2.5524
2.8784
18
19
0.1274
0.3912
0.6876
1.0655
1.3277
1.7291
2.0930
2.5395
2.8609
19
20
0.1273
0.3909
0.6870
1.0640
1.3253
1.7247
2.0860
2.5280
2.8453
20
0.6864
0.6858
0.6853
21
0.1272
0.3906
1.0627
1.3232
1.7207
2.0796
2.5176
2.8314
21
2.8188
2.8073
2.7970
22
0.1271
0.3904
1.0614
1.3212
1.7171
2.0739
2.5083
22
1,0603
1.0593
23
0.1271
0.3902
1.3195
1.7139
2.0687
2.4999
23
24
0.1270
0.3900
0.6848
1.3178
1.7109
2.0639
2.4922
24
25
0.1269
0.3898
0.6844
1.0584
1.3163
1.7081
2.0595
2.4851
2.7874
25
0.3896
0.3894
1.7056
1.7033
1.7011
26
0.1269
0.6840
1.0575
1.3150
2.0555
2.4786
2.7787
26
27
1.3137
1.3125
2.0518
2.0484
0.1268
0.6837
1.0567
2.4727
2.7707
27
28
0.1268
0.3893
0.6834
1.0560
2.4671
2.7633
28
29
0.1268
0.3892
0.6830
1.0553
1.3114
1.6991
2.0452
2.4620
2.7564
29
30
0.1267
0.3890
0.6828
1.0547
1.3104
1.6973
2.0423
2.4573
2.7500
30
40
0.1265
0.3881
0.6807
1.0500
1.3031
1.6839
2.0211
2.4233
2.7045 40
50
0.1263
0.3875
0.6794
1.0473
1.2987
1.6759
2.0086
2.4033
2.6778
50
60
0.1262
0.3872
0.6786
1.0455
1.2958
1.6706
2.0003
2.3901
2.6603
60
70
0.1261
0.3869
0.6780
1.0442
1.2938
1.6669
1.9944
2.3808
2.6479
70
80
0.1261
0.3867
0.6776
1.0432
1.2922
1.6641
1.9901
2.3739
2.6387 80
90
0.1260
0.3866
0.6772
1.0424
1.2910
1.6620
1.9867
2.3685
2.6316
90
100
0.1260
0.3864
0.6770
1.0418
1.2901
1.6602
1.9840
2.3642
2.6259 100
0.3858
0.3855
1.0386
1.0375
1.0364
0.6755
1.6510
1.6479
250
0.1258
1.2849
1.9695
2.3414
2.5956 250
500
0.1257
0.6750
1.2832
1.9647
2.3338
2.5857 500
0.1257
0.3853
0.6745
1.2816
1.6449
1.9600
2.3263
2.5758
Conf. Level
0.1
0.3
0.5
0.7
0.8
0.9
0.95
0.98
0.99 Conf. Level
One Tail
Two Tails
0.45
0.35
0.25
0.15
0.3
0.1
0.2
0.05
0.025
0.01
0.005 One Tail
0.01
0.9
0.7
0.5
0.1
0.05
0.02
Two Tails
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