In: Statistics and Probability
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 |
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