Question: A laptop computer maker uses battery packs supplied by two companies, A and B . Both brands should have the same average battery life between
A laptop computer maker uses battery packs supplied by two companies, A and B. Both brands should have the same average battery life between charges (LBC); however, the computer maker seems to receive more complaints about shorter LBC than expected for battery packs supplied by company B.If the LBC for battery packs supplied by company B is shorter than the LBC for battery packs supplied by company A, the laptop computer maker will change suppliers.
Before making any changes to their suppliers, the laptop maker wants to determine if there is any validity to the claim. Ten new battery packs from each brand were randomly selected from recent production runs and installed on the same models of laptops. The laptops were run until the battery packs were completely discharged.
Following are the observed LBCs, in hours, for each brand:
Brand A
3.2, 3.4, 2.8, 3.0, 3.0, 3.0, 2.8, 2.9, 3.0, 3.0
Brand B
3.0, 3.5, 2.9, 3.1, 2.3, 2.0, 3.0, 2.9, 3.0, 4.1
Required:
B) Using the appropriate output(s) shown below (on page 2) and the 5% level of significance:
State the research question:
State the null hypothesis
State the alternative hypothesis
Which output would you use to make a decision? Explain why.
State the decision of your hypothesis test:
C) Based on the decision of your hypothesis test (above), should the laptop computer maker make changes to the suppliers? Explain your answer.
| F-Test Two-Sample for Variances | ||
| Brand B | Brand A | |
| Mean | 2.98 | 3.01 |
| Variance | 0.33066666 | 0.03211111 |
| Observations | 10 | 10 |
| df | 9 | 9 |
| F | 10.29757785 | |
| P(F<=f) one-tail | 0.0009 | |
| F Critical one-tail | 4.025994158 |
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Brand B | Brand A | |
| Mean | 2.98 | 3.01 |
| Variance | 0.3307 | 0.0321 |
| Observations | 10 | 10 |
| Hypothesized Mean Difference | 0 | |
| df | 11 | |
| t Stat | -0.1575 | |
| P(T<=t) one-tail | 0.4388 | |
| t Critical one-tail | 1.7959 | |
| P(T<=t) two-tail | 0.8777 | |
| t Critical two-tail | 2.2010 |
| t-Test: Two-Sample Assuming Equal Variances | ||
| Brand B | Brand A | |
| Mean | 2.98 | 3.01 |
| Variance | 0.3307 | 0.0321 |
| Observations | 10 | 10 |
| Pooled Variance | 0.1814 | |
| Hypothesized Mean Difference | 0 | |
| df | 18 | |
| t Stat | -0.1575 | |
| P(T<=t) one-tail | 0.4383 | |
| t Critical one-tail | 1.7341 | |
| P(T<=t) two-tail | 0.8766 | |
| t Critical two-tail | 2.1009 |
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