Question
A researcher computes a
confidence interval for the mean weight (in lb) of widgets produced in a
factory. The interval is (
). Which of these is a correct interpretation of this interval?
a) Out of all the widgets produced in all widget factories,
weigh between 7.2 and 8.9 lbs.
b) We can be
confident that all widgets weigh between 7.2 and 8.9 lbs .
c) There’s a
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.
factory. The interval is (
a) Out of all the widgets produced in all widget factories,
b) We can be
c) There’s a
d) Ninety percent of all sample means are equivalent to the true mean weight of all the widgets.
Ask by Best Vargas. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There’s a
chance the population mean weight of widgets is between 7.2 and 8.9 lbs.
Solution
The correct interpretation of a
confidence interval for the mean weight of widgets is:
c) There’s a
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
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 chance the population value is between 7.2 and 8.9 lbs.
Option c) There’s a
Answered by UpStudy AI and reviewed by a Professional Tutor
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Mind Expander
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
confidence interval for widget weights, they’re saying that if we were to take many samples and create confidence intervals for each, approximately
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
confident that the true mean weight of the widgets falls within the interval (
). 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!