Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
The critical value that should be used in constructing the confidence interval is T = 2.898.
The 99% confidence interval for the population mean iron concentration is between 0.214 cc/cubic meter and 0.33 cc/cubic meter.
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 = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.898.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.898\frac{0.0851}{\sqrt{18}} = 0.058[/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 0.272 - 0.058 = 0.214 cc/cubic meter.
The upper end of the interval is the sample mean added to M. So it is 0.272 + 0.058 = 0.33 cc/cubic meter.
The 99% confidence interval for the population mean iron concentration is between 0.214 cc/cubic meter and 0.33 cc/cubic meter.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
