A new cell phone battery is being considered as a replacement for the current one. Ten college student cell phone users are selected to try each battery in their usual mix of "talk" and "standby" and to record the number of hours until recharge was needed. (a) Do these results show that the new battery has significantly longer life at α = .05? State your hypotheses and show all steps clearly. (b) Is the decision close? (c) Are you convinced? Battery
FIGURE 10.18
Excel's independent sample t tests
Bob May Deno Sri Pat Alexis Scott Aretha Jen Ben
New battery 45 41 53 40 43 43 49 39 41 43
Old battery 52 34 40 38 38 44 34 45 28 33

a) What are the null and alternative hypotheses to test if the new battery has longer life than the old battery?
Ho: u(new)-u(old) = 0
Ha: u(new)-u(old) > 0 (claim)
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b) Use Excel to perform the hypothesis test using alpha = 0.05.
I used a TI to get:
ts: t = 1.9646
p = 0.0341---
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c) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
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Since the p-value is less than 5% you should reject Ho.
The test result lends support to the claim that the new
batteries have longer life than the old.