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   6.16   5.88
2   16.39   9.70
3   6.33   3.86
4   11.36   10.25
5   12.43   8.57
6   7.98   6.09
7   11.42   12.81
8   13.31   19.70
9   6.83   3.57
10   9.19   3.74
11   12.73   14.83
12   13.05   12.31
13   6.98   2.65
14   12.32   11.17
15   8.82   11.89
16   9.45   3.02
17   17.65   11.26
18   9.83   6.26
19   15.09   9.11
20   6.44   8.40
21   6.38   8.82
22   20.12   18.35
23   7.57   5.92
24   13.61   8.95
25   11.08   12.47
26   5.86   3.91
27   6.67   6.09
28   9.55   9.20
29   16.08   14.36
30   2.41   1.13

In this​ example, mu Subscript d 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 0​: mu Subscript dnot equals0 Upper H 1​: mu Subscript dgreater than0

or

B. Upper H 0​: mu Subscript dnot equals0 Upper H 1​: mu Subscript dequals0

or

C. Upper H 0​: mu Subscript dequals0 Upper H 1​: mu Subscript dless than0

or

D. Upper H 0​: mu Subscript dequals0 Upper H 1​: mu Subscript dnot equals0

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 ▼ than the significance​ level, ▼ the null hypothesis. There ▼ sufficient evidence to support the claim that there is a difference between the weights of discarded paper and discarded plastic

first arrow option (less, greater)

second arrow option (fail to reject, reject)

third arrow option(is, is not)

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option D is correct.

Test statistic = 2.83

P - value = 0.008

Less; Reject; is