Question

In: Statistics and Probability

In this​ example, the amount of discarded paper and the amount of discarded plastic was collected...

In this example, the amount of discarded paper and the amount of discarded plastic was collected from a simple random sample of 30 households.

Test the claim that mean amount of discarded paper differs from the mean amount of discarded plastic. Set alpha at .05.

Review the Statdisk output and answer the following questions.

1. This output tests claims about what kind of parameter?

CH9 StatDisk paired samples t-test instructions.jpg WK14 2019 Online CH9 Discussion Image 1. This output tests claims about what kind of parameter? a. Two Proportions (Z) b. Two Independent Sample Means (t) c. Two Paired Sample Means (t) 2. What is the value of the test statistic? 3. What is/are the critical value/s? 4. Where is the critical region located? a. Right tail b. Left tail c. Two-tails 5. What is the p-value? 6. Where is the test statistic? a. Inside the rejection region b. Not in the rejection region 7. What decision should be made about the null? a. Reject the null, because the p-value is less than the alpha level b. Reject the null, because the p-value is greater than the alpha level. c. Fail to reject the null, because the p-value is less than the alpha level. d. Fail to reject the null because the, p-value is greater than the alpha level. 8. What conclusion can be made about the claim? a. There is sufficient evidence to support the claim. b. There is not sufficient evidence to support the claim. 9. Interpret the 95% confidence interval a. The 95% confidence interval includes zero, therefore there is evidence that the means differ. b. The 95% confidence interval includes zero, therefore there is not sufficient evidence that the means differ. c. The 95% confidence interval does not include zero, therefore there is sufficient evidence that the means differ. d. The 95% confidence interval does not include zero, therefore there is not sufficient evidence that the means differ.

Budget ($) in Millions Gross ($) in Millions
36 114
21 6
115 103
71 68
76 112
52 109
115 93
69 106
6 54
55 112
125 207
21 35
7 19
153 287
2 45

Solutions

Expert Solution

Budget ($) in Millions Gross ($) in Millions
36 114
21 6
115 103
71 68
76 112
52 109
115 93
69 106
6 54
55 112
125 207
21 35
7 19
153 287
2 45
Mean 61.6 98 AVERAGE()
Sd 47.91331458 72.11300655 STDEV()
15 15

1)

Two Independent Sample Means (t) why because two samples are independent samples (unknown population standard deviation)

2)

Test:

Test :
Sp^2 3747.984543 ((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)
t -1.628295114 (X1 bar-X2 bar )/SQRT(Sp^2*(1/n1 + 1/n2)) Equal vriance

3)

α= 0.05
df 28 n1+n2-2
t Critical Value :
tc 2.048407142 T.INV.2T(alpha,df) TWO

4)

Hypothesis :
Ho: μ1​ = μ2
Ha: μ1​ not = μ2

Two tailed

5)

P value = 0.1147

6)

Not in the rejection region

|ts| < tc, Do not reject H0

7)

d. Fail to reject the null because the, p-value is greater than the alpha level.

8)

b. There is not sufficient evidence to support the claim

9)

95% confidence interval

CI Equal variance
tc 2.048407142 T.INV.2T(D1,D2)
Upper 9.391465753 (X1 bar-X2 bar )+tc*Sp*SQRT(1/n1 + 1/n2)
Lower -82.19146575 (X1 bar-X2 bar )-tc*Sp*SQRT(1/n1 + 1/n2)

b. The 95% confidence interval includes zero, therefore there is not sufficient evidence that the means differ


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