7. The following data represent the battery life, in hours, for a random sample

Question

7. The following data represent the battery life, in hours, for a random sample of 10 full charges on a fifth generation iPod music player. 10.2 7.3 12.9 10.8 12.1 6.6 10.2 9.0 8.5 7.1 You may assume the data comes from a population that is normally distributed. (a) Determine the best point estimate for the mean battery life of an iPod music player. Correct notation counts. (b) Construct and interpret a 95% confidence interval for the mean number of hours the battery will last on this player. Please include formulas and show work

Explanation / Answer

A) point of estimate = (10.2 + 7.3 + 12.9 + 10.8 + 12.1 + 6.6 + 10.2 + 9 + 8.5 + 7.1)/10 = 9.47

Sample variance = ((10.2 - 9.47)^2 + (7.3 - 9.47)^2 + (12.9 - 9.47)^2 + (10.8 - 9.47)^2 + (12.1 - 9.47)^2 + (6.6 - 9.47)^2 + (10.2 - 9.47)^2 + (9 - 9.47)^2 + (8.5 - 9.47)^2 + (7.1 - 9.47)^2)/9 = 4.58

Sample standard deviation = sqrt(4.58) = 2.141

B) Degrees of freedom = 9

At 95% cinfidence interval the critical value = 2.262

Cinfidence interval = point of estimate +/- 2.262 * s/sqrt(10)

= 9.47 +/- 2.262 * 2.141/sqrt(10)

= 9.47 +/- 1.53

= 7.94, 11

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