A study is going to be conducted in which the mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval.The estimate needs to be within +/- 2 hours of the actual population mean.The population standard deviation σ is estimated to be around 25.The necessary sample size should be at least _______.
A)100
B)21
C)923
D)35
E)423

Question

Quizplus · Accepted Answer

To determine the necessary sample size for estimating the mean of a population within a certain margin of error (E) at a specified confidence level, the formula is: $n = \left(\frac{Z\sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (for 90% confidence, $Z \approx 1.645$), $\sigma$ is the population standard deviation, and $E$ is the margin of error. Plugging in the given values ($\sigma = 25$, $E = 2$), we get $n = \left(\frac{1.645 \times 25}{2}\right)^2 \approx 423$.

A Study Is Going to Be Conducted in Which the Mean