A researcher computes a \( 90 \% \) confidence interval for the mean weight (in lb) of widgets produced in a factory. The interval is ( \( 7.2,8.9 \) ). Which of these is a correct interpretation of this interval? a) Out of all the widgets produced in all widget factories, \( 90 \% \) weigh between 7.2 and 8.9 lbs. b) We can be \( 90 \% \) confident that all widgets weigh between 7.2 and 8.9 lbs . c) There's a \( 90 \% \) chance the population value is between 7.2 and 8.9 lbs . d) Ninety percent of all sample means are equivalent to the true mean weight of all the widgets.

Let's clarify this concept with a little more context! Confidence intervals are a statistical tool used to estimate the range in which the true population parameter lies. When a researcher creates a \( 90\% \) confidence interval for widget weights, they're saying that if we were to take many samples and create confidence intervals for each, approximately \( 90\% \) of those intervals would contain the true mean weight of the widgets produced in that factory. Now, if you're scratching your head over the options: the correct interpretation is that we are \( 90\% \) confident that the true mean weight of the widgets falls within the interval ( \( 7.2, 8.9 \) ). So in this case, the best answer is actually not provided in your options, but remember, confidence intervals help us understand and communicate uncertainty in our estimates! Always keep in mind that a common mistake when interpreting confidence intervals is thinking that the interval describes the weights of individual widgets or other inappropriate applications. Instead, it's all about estimating the mean, so focus on that aspect to avoid confusion!