The temperature was used to predict ice cream sales. The results show that b1=0.3943 and Sb1=0.0178. a. At the 0.05 level of significance, is there evidence of a linear relationship between temperature and ice cream sales?
The temperature was used to predict ice cream sales. The results show that b1=0.3943 and Sb1=0.0178. a. At the 0.05 level of significance, is there evidence of a linear relationship between temperature and ice cream sales?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Sales at an ice creamery are heavily reliant on the weather. A sample of the number of ice creams sold per day and the temperature in degrees Celsius was gathered for
10
days. The temperature was used to predict ice cream sales. The results show that
b1=0.3943
and
Sb1=0.0178.
a. At the 0.05 level of significance, is there evidence of a linear relationship between temperature and ice cream sales?
b. Construct a 95% confidence interval estimate of the population slope,
β1.
Click here to view page 1 of the table of the critical values of t.
LOADING...
Click here to view page 2 of the table of the critical values of t.
LOADING...
a. Determine the hypotheses for the test. Choose the correct answer below.
H0:
β0≥0
H1:
β0<0
H0:
β1=0
H1:
β1≠0
H0:
β1≥0
H1:
β1<0
H0:
β0≤0
H1:
β0>0
H0:
β0=0
H1:
β0≠0
H0:
β1≤0
H1:
β1>0
Calculate the test statistic.
t=enter your response here
(Round to two decimal places as needed.)Determine the critical value(s).
The critical value(s) is(are)
t=enter your response here.
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Reach a decision.
▼
Do not reject
Reject
H0.
There is
▼
insufficient
sufficient
b. The 95% confidence interval is
enter your response here≤β1≤enter your response here.
(Round to three decimal places as needed.)
Transcribed Image Text:Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
1.0000
0.8165
07649
07407
1
3.0777
6.3138
12.7062
31.8207
63.6574
1.8856
1.6377
2.9200
2.3534
9.9248
5.8409
4.6041
4.0322
4.3027
6.9646
4.5407
3.1824
2.7764
3.
4
1.5332
2.1318
3.7469
5
07267
1.4759
2.0150
2.5706
3.3649
07176
1.4398
1.9432
2.4469
3.1427
3.7074
1.8946
1.8595
07111
3.4905
3.3554
1.4149
2.3646
2.9980
2.8965
0.7064
0.7027
1.3968
1.3830
2.3060
2.2622
9
1.8331
2.8214
3.2498
3.1603
10
0.6998
1.3722
1.8125
2.2281
2.7638
11
0.6974
1.3634
1.7959
2.2010
2.7181
3.1058
1.7823
1.7709
1.7613
1.7531
12
0.6955
1.3562
2.1788
2.6810
3.0545
13
14
0.6038
0.6024
1.3502
1.3450
2.1604
2.1448
2.6503
2.6245
3.0123
2.9768
2.9467
15
0.6012
1.3406
2.1315
2.6025
2.5835
2.5669
25524
25395
2.1199
2.9208
2.8982
16
0.6901
1.3368
1.3334
1.7459
1.7396
0.6892
0.6884
0.6876
17
2.1098
18
19
1.3304
1.3277
1.7341
1.7291
2.1009
2.0930
2.8784
2.8609
20
0.6870
1.3253
1.7247
2.0860
25280
2.8453
1.3232
1.3212
25177
2.5083
2.4999
2.4922
2.4851
21
0.6864
1.7207
2.0796
2.8314
0.6858
0.6853
0.6848
2.8188
2.8073
2.7969
2.7874
22
1.7171
2.0739
23
24
1.7139
1.7109
1.7081
2.0687
2.0639
2.0595
1.3195
1.3178
1.3163
25
0.6844
26
0.6840
1.3150
1.7056
2.0555
2.4786
2.7787
27
28
29
30
0.6837
0.6834
0.6830
0.6828
1.3137
1.3125
1.3114
1.3104
1.7033
1.7011
1.6991
1.6973
2.0518
2.0484
2.0452
2.0423
2.4727
2.4671
2.4620
2.4573
2.7707
2.7633
2.7564
2.7500
31
1.3005
0.6825
0.6822
0.6820
0.6818
1.6955
1.6039
2.0395
2.4528
2.7740
32
1.3086
2.0369
2.4487
2.4448
2.4411
2.7385
33
34
1.3077
1.3070
1.3062
1.6924
1.6909
1.6896
2.0345
2.0322
2.7333
2.7284
2.7238
35
0.6816
2.0301
2.4377
0.6814
0.6812
0.6810
36
1.3055
1.6883
2.0281
2.0262
2.0244
2.4345
2.7195
37
38
39
1.3049
1.3042
1.6871
1.6860
2.4314
2.4286
2.7154
2.7116
2.7079
0.6808
0.6807
1.3036
1.6849
2.0227
2.0211
2.4258
40
1.3031
1.6839
2.4233
2.7045
0.6805
1.3025
1.3020
1.3016
1.3011
1.6829
1.6820
41
2.0195
2.4208
2.7012
42
0.6804
2.0181
2.4185
2.6981
43
44
0.6802
0.6801
1.6811
1.6802
2.0167
2.0154
2.0141
2.4163
2.4141
2.6951
2.6923
45
0.6800
1.3006
1.6794
2.4121
2.6896
46
0.6799
1.3022
1.6787
2.0129
2.4102
2.6870
2.6846
47
0.6797
1.2998
1.6779
2.0117
2.4083
48
0.6706
1.2904
1.6772
2.0106
2.4066
2.6822
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
Upper-tail areas
Transcribed Image Text:Upper-tail areas
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
0.6795
0.6794
2.0096
40
50
1.2991
1.2987
1.6766
2.4049
2.4033
2.6800
2.6778
1.6759
2.0086
0.6793
51
52
1.2984
1.2980
1.6753
1.6747
2.0076
2.0066
2.4017
2.4002
2.6757
2.6737
0.6792
53
0.6791
1.2977
1.6741
2.0057
2.3988
2.6718
54
55
0.6791
0.6790
1.2974
1.2971
1.6736
1.6730
2.0049
2.0040
2.3974
2.3961
2.6700
2.6682
56
57
58
59
2.0032
2.0025
2.0017
2.0010
0.6789
1.2969
1.2966
1.6725
2.3948
2.6665
0.6788
0.6787
0.6787
1.6720
1.6716
1.6711
2.3936
2.3924
2.3912
2.3901
2.6649
2.6633
1.2963
1.2961
2.6618
2.6603
60
0.6786
1.2958
1.6706
2.0003
0.6785
0.6785
0.6784
2.6589
2.6575
2.6561
61
1.2956
1.6702
1.6698
1.6604
1.6600
1.6686
1.9996
2.3890
1.2954
1.2951
2.3880
2.3870
2.3860
2.3851
62
63
1.9990
1.9983
0.6783
0.6783
1.2949
1.2947
1.9977
1.9971
2.6549
2.6536
64
65
66
67
0.6782
0.6782
1.2945
1.2943
1.6683
1.6679
1.9966
1.9960
1.9955
2.3842
2.3833
2.3824
2.6524
2.6512
2.6501
68
0.6781
1.2941
1.6676
1.2939
1.2938
69
0.6781
1.6672
1.9949
2.3816
2.6490
70
0.6780
1.6669
1.9944
2.3808
2.6479
1.6666
1.6663
1.6660
71
0.6780
1.2936
1.9939
2.3800
2.6469
72
73
0.6779
0.6779
0.6778
0.6778
2.3793
2.3785
2.3778
2.3771
2.6459
2.6440
2.6439
2.6430
1.2934
1.2933
1.9935
74
75
1.9030
1.9025
1.9921
1.2931
1.6657
1.2929
1.6654
76
77
78
79
2.3764
2.3758
2.3751
2.3745
2.3739
2.6421
2.6412
2.6403
2.6395
2.6387
0.6777
1.2928
1.6652
1.9917
0.6777
0.6776
0.6776
0.6776
1.2926
1.2925
1.2924
1.6649
1.6646
1.6644
1.9913
1.9908
1.9005
80
1.2922
1.6641
1.9001
1.2921
1.2920
1.2918
1.2917
1.2916
1.2915
1.2914
1.2912
1.2911
1.9897
1.9893
1.9890
1.9886
1.9883
2.6379
2.6371
0.6775
1.6639
2.3733
2.3727
2.3721
2.3716
2.3710
0.6775
1.6636
83
84
0.6775
0.6774
0.6774
2.6364
2.6356
2.6349
1.6634
1.6632
1.6630
2.3705
2.3700
2.6342
2.6335
2.6329
2.6322
86
87
0.6774
0.6773
0.6773
0.6773
1.6628
1.6626
1.6624
1.6622
1.9879
1.0876
1.9873
1.9870
88
80
2.3605
2.3600
2.3685
90
0.6772
1.2910
1.6620
1.9867
2.6316
91
92
93
0.6772
0.6772
0.6771
1.2909
1.2908
1.2907
1.6618
1.6616
1.9864
1.9861
1.9858
2.3680
2.3676
2.3671
2.3667
2.3662
2.6300
2.6303
2.6297
2.6291
1.6614
1.6612
94
0.6771
1.2906
1.9855
95
0.6771
1.2905
1.6611
1.9853
2.6286
1.9850
1.9847
1.9845
2.3658
2.3654
2.3650
2.3646
2.3642
06
0.6771
1.2004
1.6600
2.6280
97
98
99
0.6770
0.6770
0.6770
1.2903
1.2902
1.2902
1.2901
1.6607
1.6606
1.6604
1.6602
2.6275
2.6269
2.6264
1.9842
100
0.6770
1.9840
2.6259
110
0.6767
1.2893
1.6588
1.9818
2.3607
2.6213
120
0.6765
1.2886
1.6577
1.9799
2.3578
2.6174
0.6745
1.2816
1.6449
1.9600
2.3263
2.5758
Degrees of
freedom
0.25
0.10
0.05
0.025
0.01
0.005
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 7 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman