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.

The correct interpretation of a \( 90\% \) confidence interval for the mean weight of widgets is: **c) There's a \( 90\% \) chance the population value is between 7.2 and 8.9 lbs.** ### Explanation: A confidence interval aims to estimate the range within which the true population mean is likely to lie, based on sample data. Here's why the other options are incorrect: - **a)** This option incorrectly interprets the confidence interval as applying to individual widget weights across all factories, rather than to the population mean. - **b)** This suggests that *all* individual widgets fall within the interval, which is not the case. The confidence interval pertains to the mean, not individual measurements. - **d)** This is misleading because the confidence level refers to the proportion of intervals that would contain the true mean if the experiment were repeated many times, not to the equivalence of sample means. **Option c** accurately reflects the essence of the confidence interval: there is a \( 90\% \) probability that the true population mean lies within the specified range, based on the sample data and the confidence level chosen. **Answer:** Option c) There's a \( 90\% \) chance the population value is between 7.2 and 8.9 lbs.