Question

a random sample of cell phones has a mean battery life of 715 minutes with a margin of error of 21 minutes. interpret the meaning of the margin of error in terms of the context of the situation. (1 point)

• there can be 96 percent confidence that the sample mean is incorrect by over 21 minutes.
• there can be 96 percent confidence that the sample mean of 715 minutes is accurate.
• there can be 96 percent confidence the population of batteries has a battery life between 694 - 736 minutes.
• there can be 96 percent confidence that the sample mean is accurate for 21 minutes.

Explanation:

To interpret the margin of error, we use the concept of confidence intervals. The sample mean is 715 minutes, and the margin of error is 21 minutes. The confidence interval is calculated as sample mean ± margin of error, so \( 715 - 21 = 694 \) and \( 715 + 21 = 736 \). This means we can be (typically 95% as a common confidence level) confident that the population mean battery life lies between 694 and 736 minutes. Let's analyze the options:

• The first option is incorrect as margin of error isn't about the sample mean being incorrect by that amount.
• The second option is incorrect as margin of error isn't about the sample mean's accuracy in that way.
• The third option matches our calculation of the confidence interval (694 to 736) and the interpretation of the margin of error.
• The fourth option misinterprets the margin of error's meaning.

Answer:

There can be 95 percent confidence the population of batteries has a battery life between 694 - 736 minutes. (The option stating this, likely the third option in the list)