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

Household   Paper   Plastic
1 12.73   14.83
2 13.61   8.95
3   6.96   7.60
4 17.65   11.26
5 11.08   12.47
6 9.83   6.26
7 12.32   11.17
8 16.08   14.36
9 6.16   5.88
10    6.98   2.65
11   14.33   6.43
12 13.05   12.31
13 6.38   8.82
14 13.31   19.70
15 9.55   9.20
16 15.09   9.11
17 2.80   5.92
18 6.83   3.57
19 7.57   5.92
20 9.41   3.36
21 7.98   6.09
22 6.05   2.73
23 20.12   18.35
24 9.45   3.02
25 7.72   3.86
26   2.41   1.13
27 11.36   10.25
28 6.67   6.09
29 3.27   0.63
30    5.86   3.91

A. Identify the test statistic

B. Identify the P-value.

C. What is the conclusion based on the hypothesis​ test?

Since the​ P-value is (greater/less) than the significance​ level, (fail to reject/reject) the null hypothesis. There (is/is not) sufficient evidence to support the claim that there is a difference between the weights of discarded paper and discarded plastic.

Answer 1

The statistical software output for this problem is:

Hence,

a) Test statistic = 3.2728

b) P-value = 0.0028

c) Less; Reject; Is