A computer laboratory manager was in charge of purchasing new battery packs for

Question

A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the two models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent random samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2 Sample size 22 29 Sample mean 3 5.2 Sample std. dev. 1.8 2 Let 1 and 2 stand for population mean of lifetime for battery pack 1 and 2 respectively. Assume the variances of lifetimes are unequal. Does the data indicate that the average lifetime of battery pack 1 is different from battery pack 2?

The lower limit of 97% confidence interval for 1 2 is: (provide 3 digits after decimal)

The upper limit of 97% confidence interval for 1 2 is: (provide 3 digits after decimal)

Explanation / Answer

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=3
Standard deviation( sd1 )=1.8
Sample Size(n1)=22
Mean(x2)=5.2
Standard deviation( sd2 )=2
Sample Size(n2)=29
CI = [ ( 3-5.2) ±t a/2 * Sqrt( 3.24/22+4/29)]
= [ (-2.2) ± t a/2 * Sqrt( 0.2852) ]
= [ (-2.2) ± 2.328 * Sqrt( 0.2852) ]
= [-3.4433 , -0.9567]

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