External Power Supplies (EPCs) are used to power computers and appliances. Because computers and appliances are plugged in most of the time, power supplies for these devices should consume little energy when not in use (no-load). Until now, an average no-load power consumption of less than .50 watts for EPCs has been required to earn Energy Star certification. Starting next year, the Energy Star certification requirement will be reduced to .30 watts. In anticipation of this change, one manufacturer of EPCs has developed a new, lower consumption model to replace its current Energy Star certified model. The manufacturer has decided to test its no-load power consumption, shipping a sample of 30 new model EPCs to an accredited lab for testing. The manufacturer also sent a larger sample of 100 current model EPCs for comparison. The no-load consumption data for the two models are recorded below. a. First, compare the new model to the current model. Are the data paired or unpaired? What are the variances of the two samples? Which is the appropriate test of two means —for paired data, unpaired data with equal variances, or unpaired data with unequal variances? b. Conduct the appropriate hypothesis test to determine whether there is strong evidence that the new model has lower average no-load power consumption than the current model. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic. c. Is the hypothesis test one- or two-tailed? What is the p-value for the test statistic in (b)? d. Based on the results from (b) and (c), what is your conclusion about the difference in no-load energy consumption at α = 0.05? e. Now, focus on the new model. Conduct the appropriate test of the alternative hypothesis that the new model complies with next year’s reduced Energy Star certification requirement of .30 watts. Specifically, state the null hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test? f. What is the p-value for the test statistic in (e)? What is your conclusion about the new model’s average no-load consumption rate at α = .05? Do you expect it to be Energy Star certified? g. Compute a 98% confidence interval for the new model’s average no-load consumption. h. Is your hypothesis test conclusion from (f) consistent with the confidence interval in (g)? Why or why not? No-Load Power Consumption (Watts) New Model Previous Model 0.26 0.25 0.33 0.56 0.26 0.28 0.34 0.44 0.24 0.36 0.23 0.29 0.34 0.40 0.29 0.38 0.27 0.40 0.28 0.27 0.24 0.47 0.22 0.41 0.31 0.31 0.28 0.58 0.35 0.24 0.36 0.29 0.29 0.37 0.27 0.47 0.25 0.33 0.33 0.54 0.19 0.39 0.24 0.35 0.36 0.31 0.28 0.34 0.25 0.38 0.31 0.40 0.33 0.33 0.26 0.27 0.23 0.41 0.29 0.37 0.33 0.44 0.47 0.34 0.38 0.42 0.25 0.24 0.26 0.41 0.36 0.31 0.23 0.38 0.38 0.30 0.36 0.43 0.27 0.23 0.33 0.43 0.40 0.34 0.26 0.44 0.53 0.45 0.37 0.29 0.47 0.27 0.38 0.21 0.46 0.31 0.52 0.36 0.29 0.29 0.20 0.64 0.26 0.34 0.31 0.48 0.28 0.42 0.25 0.26 0.26 0.41 0.55 0.45 0.40 0.31 0.27 0.48 0.34 0.33 0.28 0.34 0.66 0.31 0.43 0.34 0.17 0.57 0.45 0.29 *note-show process and formulas used in EXCEL
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External Power Supplies (EPCs) are used to power computers and appliances. Because computers and appliances are plugged in most of the time, power supplies for these devices should consume little energy when not in use (no-load). Until now, an average no-load power consumption of less than .50 watts for EPCs has been required to earn Energy Star certification. Starting next year, the Energy Star certification requirement will be reduced to .30 watts. In anticipation of this change, one manufacturer of EPCs has developed a new, lower consumption model to replace its current Energy Star certified model. The manufacturer has decided to test its no-load power consumption, shipping a sample of 30 new model EPCs to an accredited lab for testing. The manufacturer also sent a larger sample of 100 current model EPCs for comparison. The no-load consumption data for the two models are recorded below.
a. First, compare the new model to the current model. Are the data paired or unpaired? What are the variances of the two samples? Which is the appropriate test of two means —for paired data, unpaired data with equal variances, or unpaired data with unequal variances?
b. Conduct the appropriate hypothesis test to determine whether there is strong evidence that the new model has lower average no-load power consumption than the current model. Specifically, state the null hypothesis and the alternative hypothesis, then compute the relevant test statistic.
c. Is the hypothesis test one- or two-tailed? What is the p-value for the test statistic in (b)?
d. Based on the results from (b) and (c), what is your conclusion about the difference in no-load energy consumption at α = 0.05?
e. Now, focus on the new model. Conduct the appropriate test of the alternative hypothesis that the new model complies with next year’s reduced Energy Star certification requirement of .30 watts. Specifically, state the null hypothesis, then compute the relevant test statistic. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test?
f. What is the p-value for the test statistic in (e)? What is your conclusion about the new model’s average no-load consumption rate at α = .05? Do you expect it to be Energy Star certified?
g. Compute a 98% confidence interval for the new model’s average no-load consumption.
h. Is your hypothesis test conclusion from (f) consistent with the confidence interval in (g)? Why or why not?
| No-Load Power Consumption (Watts) | |
| New Model | Previous Model |
| 0.26 | 0.25 |
| 0.33 | 0.56 |
| 0.26 | 0.28 |
| 0.34 | 0.44 |
| 0.24 | 0.36 |
| 0.23 | 0.29 |
| 0.34 | 0.40 |
| 0.29 | 0.38 |
| 0.27 | 0.40 |
| 0.28 | 0.27 |
| 0.24 | 0.47 |
| 0.22 | 0.41 |
| 0.31 | 0.31 |
| 0.28 | 0.58 |
| 0.35 | 0.24 |
| 0.36 | 0.29 |
| 0.29 | 0.37 |
| 0.27 | 0.47 |
| 0.25 | 0.33 |
| 0.33 | 0.54 |
| 0.19 | 0.39 |
| 0.24 | 0.35 |
| 0.36 | 0.31 |
| 0.28 | 0.34 |
| 0.25 | 0.38 |
| 0.31 | 0.40 |
| 0.33 | 0.33 |
| 0.26 | 0.27 |
| 0.23 | 0.41 |
| 0.29 | 0.37 |
| 0.33 | |
| 0.44 | |
| 0.47 | |
| 0.34 | |
| 0.38 | |
| 0.42 | |
| 0.25 | |
| 0.24 | |
| 0.26 | |
| 0.41 | |
| 0.36 | |
| 0.31 | |
| 0.23 | |
| 0.38 | |
| 0.38 | |
| 0.30 | |
| 0.36 | |
| 0.43 | |
| 0.27 | |
| 0.23 | |
| 0.33 | |
| 0.43 | |
| 0.40 | |
| 0.34 | |
| 0.26 | |
| 0.44 | |
| 0.53 | |
| 0.45 | |
| 0.37 | |
| 0.29 | |
| 0.47 | |
| 0.27 | |
| 0.38 | |
| 0.21 | |
| 0.46 | |
| 0.31 | |
| 0.52 | |
| 0.36 | |
| 0.29 | |
| 0.29 | |
| 0.20 | |
| 0.64 | |
| 0.26 | |
| 0.34 | |
| 0.31 | |
| 0.48 | |
| 0.28 | |
| 0.42 | |
| 0.25 | |
| 0.26 | |
| 0.26 | |
| 0.41 | |
| 0.55 | |
| 0.45 | |
| 0.40 | |
| 0.31 | |
| 0.27 | |
| 0.48 | |
| 0.34 | |
| 0.33 | |
| 0.28 | |
| 0.34 | |
| 0.66 | |
| 0.31 | |
| 0.43 | |
| 0.34 | |
| 0.17 | |
| 0.57 | |
| 0.45 | |
| 0.29 |
*note-show process and formulas used in EXCEL
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