Question

In: Statistics and Probability

Refer to the data set in the accompanying table. Assume that the paired sample data is...

Refer to the data set in the accompanying table. Assume that the paired sample data is a simple random sample and the differences have a distribution that is approximately normal. Use a significance level of

0.10

to test for a difference between the weights of discarded paper​ (in pounds) and weights of discarded plastic​ (in pounds).

Household   Paper   Plastic
1   5.86   3.91
2   9.83   6.26
3   9.55   9.20
4   12.43   8.57
5   6.98   2.65
6   11.42   12.81
7   7.57   5.92
8   13.31   19.70
9   6.83   3.57
10   6.38   8.82
11   16.08   14.36
12   8.72   9.20
13   6.33   3.86
14   7.98   6.09
15   6.96   7.60
16   12.32   11.17
17   14.33   6.43
18   11.08   12.47
19   3.27   0.63
20   6.16   5.88
21   2.80   5.92
22   15.09   9.11
23   13.05   12.31
24   13.61   8.95
25   9.41   3.36
26   8.82   11.89
27   9.45   3.02
28   20.12   18.35
29   6.67   6.09
30   9.19   3.74

In this​ example,

mu Subscript dμd

is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the weight of discarded paper minus the weight of discarded plastic for a household. What are the null and alternative hypotheses for the hypothesis​ test?

A.

Upper H 0H0​:

mu Subscript dμdequals=0

Upper H 1H1​:

mu Subscript dμdnot equals≠0

B.

Upper H 0H0​:

mu Subscript dμdequals=0

Upper H 1H1​:

mu Subscript dμdless than<0

C.

Upper H 0H0​:

mu Subscript dμdnot equals≠0

Upper H 1H1​:

mu Subscript dμdgreater than>0

D.

Upper H 0H0​:

mu Subscript dμdnot equals≠0

Upper H 1H1​:

mu Subscript dμdequals=0

Identify the test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is

less

greater

than the significance​ level,

fail to reject

reject

the null hypothesis. There

is not

is

sufficient evidence to support the claim that there is a difference between the weights of discarded paper and discarded plastic.

Solutions

Expert Solution

(The above calculations are obtained using R-software. The code and output are attached below).


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