The data table below contains the amounts that a sample of nine customers spent for lunch (in dollars) at a fast-food restaurant. Complete parts (a) through (d). Click here to view page 1 of the table of critical values of t. Click here to view page 2 of the table of critical values of t. 4.17 5.09 5.97 6.35 7.25 7.63 8.29 8.42 10.02 a. At the 0.10 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50? State the null and alternative hypotheses. Hou 6.50 H₁: 6.50 (Type integers or decimals. Do not include the $ symbol in your answer.) =

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
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A. Find the critical values (Round four decimal places as needed)

B. What is the test statistic? (Round four decimal places as needed)

C. What is the p-value? (Round four decimal places as needed) 

The data table below contains the amounts that a sample of nine customers spent for lunch (in dollars) at a fast-food restaurant. Complete parts (a) through (d).
Click here to view page 1 of the table of critical values of t.
Click here to view page 2 of the table of critical values of t.
4.17 5.09 5.97 6.35 7.25 7.63 8.29 8.42 10.02
a. At the 0.10 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50?
State the null and alternative hypotheses.
Ha: M = 6.50
H₁: p # 6.50
(Type integers or decimals. Do not include the $ symbol in your answer.)
Identify the critical value(s).
The critical value(s) is (are).
(Round to four decimal places as needed. Use comma to separate answers as needed.)
Transcribed Image Text:The data table below contains the amounts that a sample of nine customers spent for lunch (in dollars) at a fast-food restaurant. Complete parts (a) through (d). Click here to view page 1 of the table of critical values of t. Click here to view page 2 of the table of critical values of t. 4.17 5.09 5.97 6.35 7.25 7.63 8.29 8.42 10.02 a. At the 0.10 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50? State the null and alternative hypotheses. Ha: M = 6.50 H₁: p # 6.50 (Type integers or decimals. Do not include the $ symbol in your answer.) Identify the critical value(s). The critical value(s) is (are). (Round to four decimal places as needed. Use comma to separate answers as needed.)
Page 1 of the table of critical values of t
Q
Degrees of
Freedom
1
2
3
4
5
6
7
8
9
10
HDDHD K=%28 58822 2582252876 2
11
12
13
14
15
16
17
18
19
20
21
23
24
29
30
31
32
33
34
35
36
37
0.75
0.25
1.0000
0.8165
0.7649
0.7407
0.7267
0.7176
0.7111
0.7064
0.7027
0.6998
0.6974
0.6955
0.6938
0.6924
0.6912
0.6901
0.6892
0.6884
0.6876
0.6870
0.6864
0.6858
0.6853
0.6848
0.6844
0.6840
0.6837
0.6834
0.6830
0.6828
0.6825
0.6822
0.6820
0.6818
0.6816
0.6814
0.6812
acoin
0.90
Cumulative Probabilities
0.10
3.0777
1.8856
1.6377
1.5332
1.4759
1.4398
1.4149
1.3968
1.3830
1.3722
1.3634
1.3562
1.3502
1.3450
1.3406
1.3368
1.3334
1.3304
1.3277
1.3253
1.3232
1.3212
1.3195
1.3178
1.3163
1.3150
1.3137
1.3125
1.3114
1.3104
1.3095
1.3086
1.3077
1.3070
1.3062
1.3055
1.3049
12013
0.975
Upper-Tail Areas
0.025
12.7062
4.3027
3.1824
2.7764
2.5706
0.95
0.05
6.3138
2.9200
2.3534
2.1318
2.0150
1.9432
1.8946
1.8595
1.8331
1.8125
1.7959
1.7823
1.7709
1.7613
1.7531
1.7459
1.7396
1.7341
1.7291
1.7247
1.7207
1.7171
1.7139
1.7109
1.7081
1.7056
1.7033
1.7011
1.6991
1.6973
1.6955
1.6939
1.6924
1.6909
1.6896
1.6883
1.6871
LEOED
2.4469
2.3646
2.3060
2.2622
2.2281
2.2010
2.1788
2.1604
2.1448
2.13 15
2.1199
2.1098
2.1009
2.0930
2.0860
2.0796
2.0739
2.0687
2.0639
2.0595
2.0555
2.0518
2.0484
2.0452
2.0423
2.0395
2.0369
2.0345
2.0322
2.0301
2.0281
2.0262
2.0244
0.99
0.01
31.8207
6.9646
4.5407
3.7469
3.3649
3.1427
2.9980
2.8965
2.8214
2.7638
2.7181
2.6810
2.6503
2.6245
2.6025
2.5835
2.5669
2.5524
2.5395
2.5280
2.5177
2.5083
2.4999
2.4922
2.4851
2.4786
2.4727
2.4671
2.4620
2.4573
2.4528
2.4487
2.4448
2.4411
2.4377
2.4345
2.4314
2.1206
0.995
0.005
63.6574
9.9248
5.8409
4.6041
4.0322
3.7074
3.4995
3.3554
3.2498
3.1693
3.1058
3.0545
3.0123
2.9768
2.9467
2.9208
2.8982
2.8784
2.8609
2.8453
2.8314
2.8188
2.8073
2.7969
2.7874
2.7787
2.7707
2.7633
2.7564
2.7500
2.7440
2.7385
2.7333
2.7284
2.7238
2.7195
2.7154
27116
- X
Page 2 of the table of critical values of t
Degrees of
Freedom
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
0.75
0.25
0.6795
0.6794
0.6793
0.6792
0.6791
0.6791
0.6790
0.6789
0.6788
0.6787
0.6787
0.6786
0.6785
0.6785
0.6784
0.6783
0.6783
0.6782
0.6782
0.6781
0.6781
0.6780
0.6780
0.6779
0.6779
0.6778
0.6778
0.6777
0.6777
0.6776
0.6776
0.6776
0.6775
0.6775
0.6775
0.6774
0.6774
06771
0.90
0.10
1.2991
1.2987
1.2984
1.2980
1.2977
1.2974
1.2971
1.2969
1.2966
1.2963
1.2961
1.2958
1.2956
1.2954
1.2951
1.2949
1.2947
1.2945
1.2943
1.2941
1.2939
1.2938
1.2936
1.2934
1.2933
1.2931
1.2929
1.2928
1.2926
1.2925
1.2924
1.2922
1.2921
1.2920
1.2918
1.2917
1.2916
1 2015
Cumulative Probabilities
0.95
0.975
Upper-Tail Areas
0.025
2.0096
2.0086
0.05
1.6766
1.6759
1.6753
1.6747
1.6741
1.6736
1.6730
1.6725
1.6720
1.6716
1.6711
1.6706
1.6702
1.6698
1.6694
1.6690
1.6686
1.6683
1.6679
1.6676
1.6672
1.6669
1.6666
1.6663
1.6660
1.6657
1.6654
1.6652
1.6649
1.6646
1.6644
1.6641
1.6639
1.6636
1.6634
1.6632
1.6630
16678
2.0076
2.0066
2.0057
2.0049
2.0040
2.0032
2.0025
2.0017
2.0010
2.0003
1.9996
1.9990
1.9983
1.9977
1.9971
1.9966
1.9960
1.9955
1.9949
1.9944
1.9939
1.9935
1.9930
1.9925
1.9921
1.9917
1.9913
1.9908
1.9905
1.9901
1.9897
1.9893
1.9890
1.9886
1.9883
1.0870.
0.99
0.01
2.4049
2.4033
2.4017
2.4002
2.3988
2.3974
2.3961
2.3948
2.3936
2.3924
2.3912
2.3901
2.3890
2.3880
2.3870
2.3860
2.3851
2.3842
2.3833
2.3824
2.3816
2.3808
2.3800
2.3793
2.3785
2.3778
2.3771
2.3764
2.3758
2.3751
2.3745
2.3739
2.3733
2.3727
2.3721
2.3716
2.3710
2.2705
0.995
0.005
2.6800
2.6778
2.6757
2.6737
2.6718
2.6700
2.6682
2.6665
2.6649
2.6633
2.6618
2.6603
2.6589
2.6575
2.6561
2.6549
2.6536
2.6524
2.6512
2.6501
2.6490
2.6479
2.6469
2.6459
2.6449
2.6439
2.6430
2.6421
2.6412
2.6403
2.6395
2.6387
2.6379
2.6371
2.6364
2.6356
2.6349
2.6242
X
Transcribed Image Text:Page 1 of the table of critical values of t Q Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 HDDHD K=%28 58822 2582252876 2 11 12 13 14 15 16 17 18 19 20 21 23 24 29 30 31 32 33 34 35 36 37 0.75 0.25 1.0000 0.8165 0.7649 0.7407 0.7267 0.7176 0.7111 0.7064 0.7027 0.6998 0.6974 0.6955 0.6938 0.6924 0.6912 0.6901 0.6892 0.6884 0.6876 0.6870 0.6864 0.6858 0.6853 0.6848 0.6844 0.6840 0.6837 0.6834 0.6830 0.6828 0.6825 0.6822 0.6820 0.6818 0.6816 0.6814 0.6812 acoin 0.90 Cumulative Probabilities 0.10 3.0777 1.8856 1.6377 1.5332 1.4759 1.4398 1.4149 1.3968 1.3830 1.3722 1.3634 1.3562 1.3502 1.3450 1.3406 1.3368 1.3334 1.3304 1.3277 1.3253 1.3232 1.3212 1.3195 1.3178 1.3163 1.3150 1.3137 1.3125 1.3114 1.3104 1.3095 1.3086 1.3077 1.3070 1.3062 1.3055 1.3049 12013 0.975 Upper-Tail Areas 0.025 12.7062 4.3027 3.1824 2.7764 2.5706 0.95 0.05 6.3138 2.9200 2.3534 2.1318 2.0150 1.9432 1.8946 1.8595 1.8331 1.8125 1.7959 1.7823 1.7709 1.7613 1.7531 1.7459 1.7396 1.7341 1.7291 1.7247 1.7207 1.7171 1.7139 1.7109 1.7081 1.7056 1.7033 1.7011 1.6991 1.6973 1.6955 1.6939 1.6924 1.6909 1.6896 1.6883 1.6871 LEOED 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.13 15 2.1199 2.1098 2.1009 2.0930 2.0860 2.0796 2.0739 2.0687 2.0639 2.0595 2.0555 2.0518 2.0484 2.0452 2.0423 2.0395 2.0369 2.0345 2.0322 2.0301 2.0281 2.0262 2.0244 0.99 0.01 31.8207 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.5835 2.5669 2.5524 2.5395 2.5280 2.5177 2.5083 2.4999 2.4922 2.4851 2.4786 2.4727 2.4671 2.4620 2.4573 2.4528 2.4487 2.4448 2.4411 2.4377 2.4345 2.4314 2.1206 0.995 0.005 63.6574 9.9248 5.8409 4.6041 4.0322 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208 2.8982 2.8784 2.8609 2.8453 2.8314 2.8188 2.8073 2.7969 2.7874 2.7787 2.7707 2.7633 2.7564 2.7500 2.7440 2.7385 2.7333 2.7284 2.7238 2.7195 2.7154 27116 - X Page 2 of the table of critical values of t Degrees of Freedom 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 0.75 0.25 0.6795 0.6794 0.6793 0.6792 0.6791 0.6791 0.6790 0.6789 0.6788 0.6787 0.6787 0.6786 0.6785 0.6785 0.6784 0.6783 0.6783 0.6782 0.6782 0.6781 0.6781 0.6780 0.6780 0.6779 0.6779 0.6778 0.6778 0.6777 0.6777 0.6776 0.6776 0.6776 0.6775 0.6775 0.6775 0.6774 0.6774 06771 0.90 0.10 1.2991 1.2987 1.2984 1.2980 1.2977 1.2974 1.2971 1.2969 1.2966 1.2963 1.2961 1.2958 1.2956 1.2954 1.2951 1.2949 1.2947 1.2945 1.2943 1.2941 1.2939 1.2938 1.2936 1.2934 1.2933 1.2931 1.2929 1.2928 1.2926 1.2925 1.2924 1.2922 1.2921 1.2920 1.2918 1.2917 1.2916 1 2015 Cumulative Probabilities 0.95 0.975 Upper-Tail Areas 0.025 2.0096 2.0086 0.05 1.6766 1.6759 1.6753 1.6747 1.6741 1.6736 1.6730 1.6725 1.6720 1.6716 1.6711 1.6706 1.6702 1.6698 1.6694 1.6690 1.6686 1.6683 1.6679 1.6676 1.6672 1.6669 1.6666 1.6663 1.6660 1.6657 1.6654 1.6652 1.6649 1.6646 1.6644 1.6641 1.6639 1.6636 1.6634 1.6632 1.6630 16678 2.0076 2.0066 2.0057 2.0049 2.0040 2.0032 2.0025 2.0017 2.0010 2.0003 1.9996 1.9990 1.9983 1.9977 1.9971 1.9966 1.9960 1.9955 1.9949 1.9944 1.9939 1.9935 1.9930 1.9925 1.9921 1.9917 1.9913 1.9908 1.9905 1.9901 1.9897 1.9893 1.9890 1.9886 1.9883 1.0870. 0.99 0.01 2.4049 2.4033 2.4017 2.4002 2.3988 2.3974 2.3961 2.3948 2.3936 2.3924 2.3912 2.3901 2.3890 2.3880 2.3870 2.3860 2.3851 2.3842 2.3833 2.3824 2.3816 2.3808 2.3800 2.3793 2.3785 2.3778 2.3771 2.3764 2.3758 2.3751 2.3745 2.3739 2.3733 2.3727 2.3721 2.3716 2.3710 2.2705 0.995 0.005 2.6800 2.6778 2.6757 2.6737 2.6718 2.6700 2.6682 2.6665 2.6649 2.6633 2.6618 2.6603 2.6589 2.6575 2.6561 2.6549 2.6536 2.6524 2.6512 2.6501 2.6490 2.6479 2.6469 2.6459 2.6449 2.6439 2.6430 2.6421 2.6412 2.6403 2.6395 2.6387 2.6379 2.6371 2.6364 2.6356 2.6349 2.6242 X
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Step 1: Solution

Given information

n equals 9 space S a m p l e space s i z e
top enclose x equals fraction numerator sum for blank of x over denominator n end fraction equals fraction numerator 63.19 over denominator 9 end fraction equals 7.0211 space space S a m p l e space m e a n space

s equals square root of fraction numerator sum for blank of left parenthesis x minus top enclose x right parenthesis squared over denominator n minus 1 end fraction end root
s equals square root of fraction numerator 26.39669 over denominator 8 end fraction end root
s equals 1.816476 space space S a m p l e space s tan d a r d space d e v i a t i o n s space
mu equals 6.50 space P o p u l a t i o n space m e a n spacen=

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