Question

Brand A   Brand B
3,202   3,792
3,135   3,653
3,131   3,649
3,202   3,702
3,256   3,748
3,260   3,686
3,255   3,693
3,234   3,666
3,088   3,666
3,130   3,646
3,113   3,723
3,132   3,696
3,114   3,700
3,090   3,652
3,115   3,743
3,073   3,697
3,116   3,660
3,098   3,668
3,156   3,720
3,143   3,641
3,140   3,628
3,153   3,699
3,133   3,691
3,098   3,704
3,088   3,658
3,191   3,683
3,187   3,693
3,114   3,684
3,175   3,687
3,157   3,711
3,112   3,682
3,190   3,726
3,147   3,665
3,173   3,703
3,164   3,754
3,123   3,715
3,145   3,709
3,151   3,729
3,157   3,751
3,154   3,774
3,169   3,757
3,178   3,732
3,215   3,639
3,165   3,705
3,169   3,745
3,133   3,733
3,082   3,718
3,104   3,710
3,141   3,703
3,134   3,734
3,164   3,742
3,159   3,737
3,119   3,727
3,040   3,642
3,196   3,684
3,154   3,698
3,145   3,683
3,172   3,694
3,130   3,688
3,154   3,686
3,199   3,717
3,184   3,690
3,196   3,676
3,134   3,614
3,177   3,667
3,189   3,647
3,184   3,666
3,150   3,678
3,172   3,680
3,147   3,679
3,138
3,173
3,109
3,116
3,146

Studies conducted by the manufacturer of two different brands of asphalt shingles have shown product weight to be a major factor in the​ customer's perception of quality. The accompanying table shows the weight​ (in pounds) from a sample of 75 pallets of brand A shingles and 70 pallets of brand B shingles. Complete parts​ (a) through​ (e) below.

a. For the brand A​ shingles, is there evidence at the .01 level of significance that the population weight is different from 3,140 pounds?

Determine the Null Hypothesis H₀ And the alternative hypothesis, H₁

Determine the test statistic

Determine the P-Value

State the conclusion.

b. Interpret the meaning of the p-value in (a). Select the correct choice below and fill in the answer boy to complete your choice.

(Rounding to one decimal place)

A. There is a _% chance the null hypothesis is true.

B. If the population mean weight is in fact 3,140 pounds, there is a _% chance of observing a sample of 75 pallets that will yield a test statistic more extreme than the test statistic for this sample.

C. There is a _% chance that the alternative hypothesis is true

D. If the population mean weight is in fact not equal to 3,140, there is a _% chance of observing a sample of 75 pallets that will yield a test statistic more extreme then the test statistic in this sample.

c. For the brand B Shingles is there evidence at the .01 level of significance that the population mean weight is different from the 3,680 pounds?

Determine the Null Hypothesis H₀ And the alternative hypothesis, H₁

Determine the test statistic

Determine the P-Value

State the conclusion.

d. Interpret the meaning of the​ p-value in​ (b). round to 1 decimal place.

e. In (a) Through (d) do you have to be concerned with the normality assumption? Explain

Answer 1

In order to solve this question I used R software.

R codes and output:

Que.a

> A=scan('clipboard');A
Read 75 items
[1] 3202 3135 3131 3202 3256 3260 3255 3234 3088 3130 3113 3132 3114 3090 3115
[16] 3073 3116 3098 3156 3143 3140 3153 3133 3098 3088 3191 3187 3114 3175 3157
[31] 3112 3190 3147 3173 3164 3123 3145 3151 3157 3154 3169 3178 3215 3165 3169
[46] 3133 3082 3104 3141 3134 3164 3159 3119 3040 3196 3154 3145 3172 3130 3154
[61] 3199 3184 3196 3134 3177 3189 3184 3150 3172 3147 3138 3173 3109 3116 3146
> B=scan('clipboard');B
Read 70 items
[1] 3792 3653 3649 3702 3748 3686 3693 3666 3666 3646 3723 3696 3700 3652 3743
[16] 3697 3660 3668 3720 3641 3628 3699 3691 3704 3658 3683 3693 3684 3687 3711
[31] 3682 3726 3665 3703 3754 3715 3709 3729 3751 3774 3757 3732 3639 3705 3745
[46] 3733 3718 3710 3703 3734 3742 3737 3727 3642 3684 3698 3683 3694 3688 3686
[61] 3717 3690 3676 3614 3667 3647 3666 3678 3680 3679
> t.test(A,mu=3140,conf.level=0.99)

One Sample t-test

data: A
t = 2.302, df = 74, p-value = 0.02415
alternative hypothesis: true mean is not equal to 3140
99 percent confidence interval:
3138.352 3163.834
sample estimates:
mean of x
3151.093

Hypothesis:

t_STAT = 2.30

p-value = 0.024

Since p-value is greater than 0.01.

Fail to reject (accept) H₀. There is sufficient evidence that the population mean weight is equal to 3140 pounds.

Que.b

If the population mean weight is in fact not equal to 3,140, there is a 99% chance of observing a sample of 75 pallets that will yield a test statistic more extreme then the test statistic in this sample.

Que.c

> t.test(B,mu=3680,conf.level=0.99)

One Sample t-test

data: B
t = 3.7197, df = 69, p-value = 0.0004025
alternative hypothesis: true mean is not equal to 3680
99 percent confidence interval:
3684.597 3707.346
sample estimates:
mean of x
3695.971

Hypothesis:

t_STAT = 3.72

p-value = 0.000

Que.d

Since p-value is less than 0.01,  

Reject H₀. There is insufficient evidence that the population mean weight is equal to 3680 pounds.

Que.e

Since sample size is large, hence distribution of test statistics approximately follows normal distribution.