A store owner wants to check whether his competitor, Moe's Monster Market, carries larger produce than he does. He purchased 100 randomly selected kiwis from Moe's and weighed them. The owner found a 95% confidence interval of for the mean weight of kiwis from Moe's (in grams). Is the following conclusion valid? If 100 more samples are taken (with elements chosen randomly and independently), it is expected that exactly 95 of them will each produce a 95% confidence interval that contains its sample mean. Choices: (A)yes (B)no

Common Misconception: The statement is a common misconception about confidence intervals. A 95% confidence interval means that if we were to take many samples and build a confidence interval from each, we would expect about 95% of those intervals to contain the true population mean, not the sample mean.Incorrect Conclusion: The conclusion that exactly 95 out of 100 additional samples will produce a 95% confidence interval containing their sample mean is incorrect. Each sample mean may or may not be within its own confidence interval, and the intervals are about the population mean, not the sample means.Correct Interpretation: The correct interpretation is that we are 95% confident that the true population mean lies within the calculated confidence interval from the original sample. This does not guarantee the same for additional samples.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A store owner wants to check whether his competitor, Moe's Monster Market, carries larger produce than he does. He purchased $100$ randomly selected kiwis from Moe's and weighed them. The owner found a $95\%$ confidence interval of for the mean weight of kiwis from Moe's (in grams). $\newline$ Is the following conclusion valid? $\newline$ If $100$ more samples are taken (with elements chosen randomly and independently), it is expected that exactly $95$ of them will each produce a $95\%$ confidence interval that contains its sample mean. $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

View step-by-step help

Home

Math Problems

Algebra 2

Interpret confidence intervals for population means

Full solution

Q. A store owner wants to check whether his competitor, Moe's Monster Market, carries larger produce than he does. He purchased

100

randomly selected kiwis from Moe's and weighed them. The owner found a

95\%

confidence interval of for the mean weight of kiwis from Moe's (in grams).

\newline

Is the following conclusion valid?

\newline

100

more samples are taken (with elements chosen randomly and independently), it is expected that exactly

95

of them will each produce a

95\%

confidence interval that contains its sample mean.

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Common Misconception: The statement is a common misconception about confidence intervals. A $95\%$ confidence interval means that if we were to take many samples and build a confidence interval from each, we would expect about $95\%$ of those intervals to contain the true population mean, not the sample mean.
Incorrect Conclusion: The conclusion that exactly $95$ out of $100$ additional samples will produce a $95\%$ confidence interval containing their sample mean is incorrect. Each sample mean may or may not be within its own confidence interval, and the intervals are about the population mean, not the sample means.
Correct Interpretation: The correct interpretation is that we are $95\%$ confident that the true population mean lies within the calculated confidence interval from the original sample. This does not guarantee the same for additional samples.