Save \& Exit Certify Lesson: 8.1 Estimating Population vieair 3/14 Question 4 of 14, Step 1 of 1 Correct The mean number of hours of part-time work per week for a sample of 93 teenagers is 21 . If the margin of error for the population mean with a \( 98 \% \) confidence interval is 1.4 , construct a \( 98 \% \) confidence interval for the mean number of hours of part-time work per week for all teenagers. Tables Keypad Answer How to enter your answer (opens in new window) Keyboard Shortcuts

To create a \( 98 \% \) confidence interval, you start with the sample mean and then apply the margin of error. Here, the sample mean is 21 hours, and the margin of error is 1.4 hours. You would subtract and add the margin of error from the sample mean to get the lower and upper bounds of the confidence interval. So, the interval will be \( 21 - 1.4 = 19.6 \) and \( 21 + 1.4 = 22.4 \). Therefore, the \( 98 \% \) confidence interval for the mean number of hours of part-time work per week for all teenagers is \( (19.6, 22.4) \). Now, isn’t it fascinating how statistics can help us understand a larger group based on a sample? This is the magic of inferential statistics! Essentially, by sampling just 93 teenagers, we’re gaining insights into the work habits of potentially millions. This method allows businesses, educators, and policymakers to make informed decisions that can greatly impact the community. When constructing confidence intervals, one common mistake is to forget that the mean and margin of error are critical to accurately forming the interval. People sometimes mistakenly add or subtract the wrong values, leading to an unreliable interval. To avoid this, always double-check your calculations and ensure that you clearly understand the relationship between the sample mean, margin of error, and the resulting interval!