The following data show the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Li-ion NiMH 109 85 97 90 89 88 86 87 91 87 100 86 97 85 87 89 86 90 98 84 99 86 102 88 88 90 104 88 89 96 80
Two-Sample t-Test and Confidence Interval
The following data show the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries.
| Li-ion | NiMH |
|---|---|
| 109 | 85 |
| 97 | 90 |
| 89 | 88 |
| 86 | 87 |
| 91 | 87 |
| 100 | 86 |
| 97 | 85 |
| 87 | 89 |
| 86 | 90 |
| 98 | 84 |
| 99 | 86 |
| 102 | 88 |
| 88 | 90 |
| 104 | 88 |
| 89 | |
| 96 | |
| 80 |
Perform a hypothesis test using significance level (α) = 0.03 to determine if the true average number of minutes per charge for NiMH batteries is different from that for Li-ion batteries.
a. Use Excel to create histogram for each sample and side-by-side boxplots for the two samples of the given data.
Based on the graphs you created in Excel and the given information, why the two-sample t-test is valid for this study? (select all that are true).
_____The samples are not independent.
_____The sample size is not large enough.
_____The samples are not random.
_____We can reasonably assume that each population has a
_____The sample data contain at least one outlier.
______We cannot reasonably assume that each population has a normal distribution because samples do not have approximately a normal distributions.
______The samples are random and independent.
______The sample data contain no outliers.
b. Use Excel to perform a two-sample t test to test the claim that the true average number of minutes per charge for Li-ion batteries is different from that for NiMH batteries.
Based on your Excel work, answer the following questions.
The observed difference in mean number of minutes per charge between Li-ion and NiMH batteries is (rounded to 4 decimal places) _______________
The p-value for this test is (rounded to 4 decimal places) __________________
At 0.03 significance level, the correct conclusion for this test is
_______There is enough evidence that the true average number of minutes per charge for NiMH batteries is different from that for Li-ion batteries.
_______There is NO enough evidence that the true average number of minutes per charge for NiMH batteries is different from that for Li-ion batteries.
_______None of these.
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