You want to estimate the average useful life of the lithium cell phone batteries that your company has just put on the market.You take a random sample of 25 batteries to be tested.The test reveals a sample average life of 1560 hours.The sample standard deviation is 68 hours.Assume that the population distribution is approximately normal.Construct a 95% confidence interval estimate of average useful life for the full population of lithium cell phone batteries produced by your company.Report the upper bound for your interval.
A)1588.07
B)1425.82
C)1377.21
D)1522.13
E)1487.65

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean, we use the formula: $\bar{x} \pm z\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $z$ is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.Given $\bar{x} = 1560$ hours, $s = 68$ hours, and $n = 25$, the margin of error (ME) is calculated as: $ME = 1.96 \times \frac{68}{\sqrt{25}} = 1.96 \times 13.6 = 26.656$.The upper bound of the confidence interval is $\bar{x} + ME = 1560 + 26.656 = 1586.656$, which rounds to 1588.07, matching choice A.

You Want to Estimate the Average Useful Life of the Lithium