A smartphone company has to decide which battery they will use for their upcomin

Question

A smartphone company has to decide which battery they will use for their upcoming model. Two battery manufacturers A and Bare competing to get the contract. 15 smartphones ofthe upcoming model were tested with batteries from A. The talktime on a single charge for them has a sample mean of 7.2 hours and sample variance of 2.7. 31 smartphones of the upcomingmodel were tested with batteries from B. The talktime on a single charge for them has a sample mean of 6.8 hours and sample variance of 2.9. Assume that the talktime on a single charge for batteries made by A and B are both normally distributed. Based on the dataset, answer the next 4 questions:

Explanation / Answer

Q.3 Null Hypothesis : H0 : The Battery A talktime on the single charge is more than one hour compared to the Battery B talktime om simgle charge. A - B >1

Alternative Hypothesis : Ha : The Battery A talktime on the single charge is not more than one hour compared to the Battery B talktime om simgle charge. A - B =< 1

Pooled standard deviation for both batteries

sp = sqrt [(nA -1) sA2 + (n2 -1)sB2 ]/ (nA +nB -2) = sqrt[14 * 2.7+ 30 * 2.9] /[14 + 30] = 1.6842

Test Statistic

t = [(xA -xB)- (A - B )H ]/ sp sqrt [1/n1 +1/n2 ] = [(7.2 - 6.8) - 1]/ 1.6842 * sqrt [1/15 + 1/31 ]

= -0.6/ 0.53= -1.13

so P - value = 0.15 approx.

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