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# The manufacturer of Boston and Vermont asphalt shingles knows that product weight is a major factor in the customer's perception of quality....

The manufacturer of Boston and Vermont asphalt shingles knows that product weight is a major factor in the customer’s perception of quality. Moreover, the weight represents the amount of raw materials being used and is therefore very important to the company from a cost standpoint. The last stage of the assembly line packages the shingles before they are placed on wooden pallets. Once a pallet is full (a pallet for most brands holds 16 squares of shingles), it is weighed, and the measurement is recorded. The data file (Pallet) contains the weight (in pounds) from a sample of 368 pallets of Boston shingles and 330 pallets of Vermont shingles. Completely analyze the differences in the weights of the Boston and Vermont shingles, using α = 0.05.
File (Pallet):
Boston Vermont
3202 3792
3134 3652
3134 3652
3226 3726
3236 3728
3250 3676
3266 3704
3224 3656
3088 3666
3132 3648
3098 3708
3118 3682
3094 3680
3108 3670
3100 3728
3084 3708
3134 3678
3090 3660
3154 3718
3138 3636
3156 3644
3138 3684
3130 3688
3118 3724
3112 3682
3168 3660
3166 3672
3122 3692
3160 3672
3146 3700
3124 3694
3170 3706
3132 3650
3162 3692
3156 3746
3136 3728
3162 3726
3136 3714
3136 3730
3148 3768
3152 3740
3166 3720
3202 3626
3152 3692
3154 3730
3126 3726
3098 3734
3106 3712
3122 3684
3118 3718
3164 3742
3158 3736
3122 3730
3064 3666
3176 3664
3144 3688
3156 3694
3162 3684
3130 3688
3156 3688
3184 3702
3170 3676
3176 3656
3152 3632
3162 3652
3200 3658
3202 3684
3142 3670
3170 3678
3142 3674
3154 3674
3158 3634
3106 3684
3136 3708
3170 3670
3124 3684
3174 3746
3160 3688
3162 3702
3160 3666
3118 3670
3138 3700
3132 3658
3140 3664
3134 3682
3166 3672
3122 3730
3154 3712
3130 3720
3106 3700
3092 3722
3136 3728
3150 3692
3138 3726
3214 3686
3092 3708
3162 3732
3126 3724
3086 3730
3112 3698
3138 3686
3118 3680
3156 3732
3156 3718
3144 3700
3160 3718
3166 3666
3172 3714
3134 3706
3186 3718
3146 3712
3144 3688
3124 3736
3122 3706
3116 3720
3126 3714
3140 3740
3110 3724
3128 3744
3114 3728
3138 3728
3106 3680
3142 3652
3128 3634
3142 3640
3144 3728
3122 3724
3046 3704
3062 3668
3114 3684
3100 3652
3126 3756
3088 3702
3140 3840
3140 3696
3120 3702
3132 3732
3130 3736
3140 3752
3114 3696
3108 3732
3146 3702
3172 3640
3102 3672
3120 3756
3102 3710
3132 3736
3120 3726
3088 3800
3084 3784
3120 3804
3098 3740
3096 3730
3088 3778
3092 3718
3062 3810
3084 3786
3136 3766
3080 3736
3056 3738
3064 3726
3088 3764
3110 3678
3096 3728
3094 3716
3080 3856
3074 3816
3114 3792
3136 3808
3104 3802
3080 3746
3104 3800
3082 3780
3080 3756
3074 3768
3095 3768
3098 3728
3084 3724
3086 3736
3074 3760
3092 3708
3062 3688
3108 3650
3132 3636
3122 3628
3078 3656
3180 3630
3076 3730
3072 3662
3114 3746
3080 3726
3102 3702
3074 3678
3148 3676
3112 3738
3112 3598
3118 3718
3118 3738
3094 3766
3076 3750
3050 3740
3100 3784
3114 3760
3100 3804
3104 3798
3088 3804
3148 3714
3088 3720
3074 3760
3074 3650
3094 3686
3116 3750
3104 3690
3100 3686
3112 3718
3098 3732
3086 3702
3098 3706
3136 3660
3100 3686
3122 3650
3132 3678
3120 3708
3096 3706
3100 3646
3114 3698
3128 3644
3084 3642
3098 3746
3104 3714
3124 3674
3130 3626
3088 3592
3110 3642
3126 3646
3116 3734
3110 3654
3148 3672
3082 3684
3142 3692
3116 3676
3092 3666
3106 3640
3102 3704
3096 3650
3078 3616
3116 3706
3164 3770
3124 3740
3102 3726
3120 3706
3114 3756
3086 3724
3160 3718
3172 3706
3164 3654
3176 3730
3124 3734
3102 3704
3164 3734
3152 3662
3144 3640
3146 3618
3166 3644
3096 3586
3146 3566
3134 3674
3128 3842
3176 3764
3166 3650
3186 3652
3158 3740
3136 3814
3124 3754
3196 3714
3178 3634
3150 3626
3160 3658
3092 3672
3122 3662
3116 3662
3122 3666
3128 3732
3172 3710
3164 3648
3066 3714
3116 3748
3132 3732
3124 3658
3148 3680
3138 3762
3118 3636
3098 3700
3132 3754
3062 3756
3116 3652
3148 3700
3122 3664
3140 3672
3134 3658
3166 3750
3136 3662
3068 3762
3134 3742
3116 3788
3152 3668
3124 3658
3106 3726
3080 3704
3092 3654
3142 3684
3112 3774
3094 3770
3092 3788
3132 3646
3118 3660
3152 3696
3124 3704
3146 3722
3098 3682
3168 3636
3174 3630
3106 3630
3184 3728
3134 3692
3104 3688
3140 3694
3108 3694
3098 3744
3186 3734
3180
3122
3124
3148
3166
3080
3112
3144
3142
3112
3094
3066
3136
3128
3072
3090
3080
3092
3076
3098
3102
3076
3044
3112
3092
3094
3066
3098
3082
3146
3144
3098
3068
3098
3140
3130
3088
3082

a/ for the boston shingles, is there evidence that the population mean weight is different from 3150 pounds?
b/ interpret the meaning of the p-value in (a)
c/ for the vermont shingles, is there evidence that the population mean weight is different from 3700 pounds?
d/ interpret the meaning of the p-value in (c)
e/ in (a) though (d) do you have to worry about the normality assumption? explain

The manufacturer of Boston and Vermont asphalt shingles knows that product weight is a major
factor in the customer’s perception of quality. Moreover, the weight represents the amount of raw
materials being used and is therefore very important to the company from a cost standpoint. The
last stage of the assembly line packages the shingles before they are placed on wooden pallets.
Once a pallet is full (a pallet for most brands holds 16 squares of shingles), it is weighed, and the
measurement is recorded. The data file (Pallet) contains the weight (in pounds) from a sample of
368 pallets of Boston shingles and 330 pallets of Vermont shingles. Completely analyze the
differences in the weights of the Boston and Vermont shingles, using α = 0.05.
File (Pallet):
Boston
Vermont
3202
3792
3134
3652
3134
3652
3226
3726
3236
3728
3250
3676
3266
3704
3224
3656
3088
3666
3132
3648
3098
3708
3118
3682
3094
3680
3108
3670
3100
3728
3084
3708
3134
3678
3090
3660
3154
3718
3138
3636
3156
3644
3138
3684
3130
3688
3118
3724
3112
3682
3168
3660
3166
3672
3122
3692
3160
3672
3146
3700
3124
3694
3170
3706
3132
3650
3162
3692
3156
3746
3136
3728 3162
3136
3136
3148
3152
3166
3202
3152
3154
3126
3098
3106
3122
3118
3164
3158
3122
3064
3176
3144
3156
3162
3130
3156
3184
3170
3176
3152
3162
3200
3202
3142
3170
3142
3154
3158
3106
3136
3170
3124
3174
3160
3162
3160
3118
3138 3726
3714
3730
3768
3740
3720
3626
3692
3730
3726
3734
3712
3684
3718
3742
3736
3730
3666
3664
3688
3694
3684
3688
3688
3702
3676
3656
3632
3652
3658
3684
3670
3678
3674
3674
3634
3684
3708
3670
3684
3746
3688
3702
3666
3670
3700 3132
3140
3134
3166
3122
3154
3130
3106
3092
3136
3150
3138
3214
3092
3162
3126
3086
3112
3138
3118
3156
3156
3144
3160
3166
3172
3134
3186
3146
3144
3124
3122
3116
3126
3140
3110
3128
3114
3138
3106
3142
3128
3142
3144
3122
3046 3658
3664
3682
3672
3730
3712
3720
3700
3722
3728
3692
3726
3686
3708
3732
3724
3730
3698
3686
3680
3732
3718
3700
3718
3666
3714
3706
3718
3712
3688
3736
3706
3720
3714
3740
3724
3744
3728
3728
3680
3652
3634
3640
3728
3724
3704 3062
3114
3100
3126
3088
3140
3140
3120
3132
3130
3140
3114
3108
3146
3172
3102
3120
3102
3132
3120
3088
3084
3120
3098
3096
3088
3092
3062
3084
3136
3080
3056
3064
3088
3110
3096
3094
3080
3074
3114
3136
3104
3080
3104
3082
3080 3668
3684
3652
3756
3702
3840
3696
3702
3732
3736
3752
3696
3732
3702
3640
3672
3756
3710
3736
3726
3800
3784
3804
3740
3730
3778
3718
3810
3786
3766
3736
3738
3726
3764
3678
3728
3716
3856
3816
3792
3808
3802
3746
3800
3780
3756 3074
3095
3098
3084
3086
3074
3092
3062
3108
3132
3122
3078
3180
3076
3072
3114
3080
3102
3074
3148
3112
3112
3118
3118
3094
3076
3050
3100
3114
3100
3104
3088
3148
3088
3074
3074
3094
3116
3104
3100
3112
3098
3086
3098
3136
3100 3768
3768
3728
3724
3736
3760
3708
3688
3650
3636
3628
3656
3630
3730
3662
3746
3726
3702
3678
3676
3738
3598
3718
3738
3766
3750
3740
3784
3760
3804
3798
3804
3714
3720
3760
3650
3686
3750
3690
3686
3718
3732
3702
3706
3660
3686 3122
3132
3120
3096
3100
3114
3128
3084
3098
3104
3124
3130
3088
3110
3126
3116
3110
3148
3082
3142
3116
3092
3106
3102
3096
3078
3116
3164
3124
3102
3120
3114
3086
3160
3172
3164
3176
3124
3102
3164
3152
3144
3146
3166
3096
3146 3650
3678
3708
3706
3646
3698
3644
3642
3746
3714
3674
3626
3592
3642
3646
3734
3654
3672
3684
3692
3676
3666
3640
3704
3650
3616
3706
3770
3740
3726
3706
3756
3724
3718
3706
3654
3730
3734
3704
3734
3662
3640
3618
3644
3586
3566 3134
3128
3176
3166
3186
3158
3136
3124
3196
3178
3150
3160
3092
3122
3116
3122
3128
3172
3164
3066
3116
3132
3124
3148
3138
3118
3098
3132
3062
3116
3148
3122
3140
3134
3166
3136
3068
3134
3116
3152
3124
3106
3080
3092
3142
3112 3674
3842
3764
3650
3652
3740
3814
3754
3714
3634
3626
3658
3672
3662
3662
3666
3732
3710
3648
3714
3748
3732
3658
3680
3762
3636
3700
3754
3756
3652
3700
3664
3672
3658
3750
3662
3762
3742
3788
3668
3658
3726
3704
3654
3684
3774 3094
3092
3132
3118
3152
3124
3146
3098
3168
3174
3106
3184
3134
3104
3140
3108
3098
3186
3180
3122
3124
3148
3166
3080
3112
3144
3142
3112
3094
3066
3136
3128
3072
3090
3080
3092
3076
3098
3102
3076
3044
3112
3092
3094
3066
3098 3770
3788
3646
3660
3696
3704
3722
3682
3636
3630
3630
3728
3692
3688
3694
3694
3744
3734 3082
3146
3144
3098
3068
3098
3140
3130
3088
3082
a/ for the boston shingles, is there evidence that the population mean weight is different from
3150 pounds?
b/ interpret the meaning of the p-value in (a)
c/ for the vermont shingles, is there evidence that the population mean weight is different from
3700 pounds?
d/ interpret the meaning of the p-value in (c)
e/ in (a) though (d) do you have to worry about the normality assumption? explain

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## This question was asked on Nov 13, 2010 and answered on Nov 13, 2010.

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