Question

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New Battery Old Difference Battery (New-Old) Student Bob May Deno 52 4. (14 points) A new cell phone battery is being considered as a replacement for the current one. Ten randomly selected college student cell phone users are selected to try cach battery in their usual mix of "talk" and "standby" and to record the number of hours until recharge was needed. Do the results show that the new battery has a significantly longer life (use a=0.05 and assume that the normality assumption is satisfied)? Remember to show all of the necessary calculations to receive full credit. Answer: The new battery does / does not (circle one) have a significantly longer battery life. 41 40 Sri 38 Pat Alexis Scott Aretha Jen Ben - - - นว นงง Sum Mean Median Variance 437 43.7 43.0 18.678 33 386 38.6 38.0 48.711 6.0 62.989

Answer 1

Student	New battery	Old battery	Difference(New-old)
bob	45	52	-7
may	41	34	7
deno	53	40	13
sri	40	38	2
pat	43	38	5
alexis	43	44	-1
scott	49	34	15
aretha	39	45	-6
jen	41	28	13
ben	43	33	10
total	437	386	51
mean=total/n	437/10=43.7	386/10=38.6	51/10=5.1
median	43	38	6
variance	18.678	48.711	62.989

To test whether the new battery have long life or not.

first we do the mean difference test,

Hypotheses,

HOM1 =
versus
2117 11:TH

the test statistic is given by,

Hi - M2 - 0 s1a/n + s22 /n

degrees of freedom = n-1 = 9

5.1 18.6782/10 + 48.7112/10

= 1.9646

at $\alpha$ = 0.05,

Hence, we failed to reject the null hypothesis.

Next we're to test hypotheses,

$H_{0}:s1^{2}=s2^{2}$ versus

Hi: s1+ s2

the test statistic is given by,

F = s1² / s2²

= 18.678/48.711 = 0.3834

we reject the null hypothesis if

F> Fa/2,9.9

for $\alpha$=0.05 , = 4.03

Fa/2.9.9

Hence, we failed to reject the null hypothesis.

therefore, The new battery doesn't have a significantly longer battery life.

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