Question

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.

Answer 1

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