1. Question: The average number of onions needed to make French onion soup from a population of recipes is unknown. A random sample of recipes yields a sample mean of x¯=8.2 onions. Assume the sampling distribution of the mean has a standard deviation of σx¯=2.3 onions.
Use the Empirical Rule t...
Confidence Intervals – Empirical Rule
Week 6
1. The average number of onions needed to make French onion soup from a
population of recipes is unknown. A random sample of recipes yields a
sample mean of x¯=8.2 onions. Assume the sampling distribution of the
mean has a standard deviation of σx¯=2.3 onions.
Use the Empirical Rule to construct a 95% confidence interval for the true
population mean number of onions.
(x¯−z⋅σx¯,x¯+z⋅σx¯)(8.2−2⋅2.3,8.2+2⋅2.3)(8.2−4.6,8.2+4.6)
(3.6,12.8)
2. In a random sample of 30 young bears, the average weight at the age of breeding is
312 pounds. Assuming the population ages are normally distributed with a population
standard deviation is 30 pounds, use the Empirical Rule to construct a 68% confidence
interval for the population average of young bears at the age of breeding. Do not round
intermediate calculations. Round only the final answer to the nearest pound. Remember to
enter the smaller value first, then the larger number. (307,317)
3. A random sample of garter snakes were measured and the proportion of
snakes that were longer than 20 inches in length recorded. The
measurements resulted in a sample proportion of p′=0.25, with a sampling
standard deviation of σp′=0.05.
Write a 68% confidence interval for the true proportion of garter snakes
that are over 20 inches in length (p′−z⋅σp′,p′+z⋅σp′)
(0.25−1⋅0.05,0.25+1⋅0.05)(0.25−0.05,0.25+0.05)
(0.20,0.30)
4. The average height of a population is unknown. A random sample from
the population yields a sample mean of x¯=66.3 inches. Assume the
sampling distribution of the mean has a standard deviation of σx¯=0.8
inches.
Use the Empirical Rule to construct a 95% confidence interval for the true
population mean height.
= (64.7, 67.9)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Milestonee. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £15.49. You're not tied to anything after your purchase.
