Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Answer:
The critical value that should be used in constructing the confidence interval is T = 1.316.
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 26 - 1 = 25
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.8}{2} = 0.9[/tex]. So we have T = 1.316
The critical value that should be used in constructing the confidence interval is T = 1.316.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds
The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.
The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.