6) A new cell phone battery is being considered as a replacement for the current

Question

6) 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) State the Hypothesis to test if the new battery has longer life than the old battery?

b) Choose a level of Use = 0.05 for this problem.

c) The data appear in the Battery worksheet of the HW2 data workbook on Moodle. Collect data and calculate necessary statistics to test the hypothesis.

d) Sketch the sampling distribution. Include the critical value and test statistic.

e) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

f) What is the p-value for the hypothesis test?

g) Use Excel to perform the hypothesis test.

Participant New Battery Old Battery Bob 45 52 May 41 34 Deno 53 40 Sri 40 38 Pat 43 38 Alexis 43 44 Scott 49 34 Aretha 39 45 Jen 41 28 Ben 43 33

Explanation / Answer

Solution :

New :

Old :

( a )

The null and alternative hypotheses to test if the new battery has longer life than the old battery is :

( d )

Critical value : = 0.05, df = 10+10-2 = 18, so the critical value is 1.734

Test statistic : t = (43.7 - 38.6)/(5.805 * sqrt(2/10)) = 1.965

( e )

Conclusion : Reject the null hypothesis, since the calculated value of test statistic is greater than the critical value. The sample provides enough evidence to support the claim that the new battery has significantly longer life.

( f )

The p-value for the hypothesis test is 0.0326

New :

n 10 mean 43.7 standard deviation 4.321779469

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