Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Using the t-distribution to build the 99% confidence interval, it is found that:
- The margin of error is of 3.64.
- The 99% confidence interval for the population mean is (19.36, 26.64).
What is a t-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
- [tex]\overline{x}[/tex] is the sample mean.
- t is the critical value.
- n is the sample size.
- s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.
The other parameters are given as follows:
[tex]\overline{x} = 23, s = 8, n = 21[/tex]
The margin of error is given by:
[tex]M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - M = 23 - 3.64 = 19.36[/tex]
[tex]\overline{x} + M = 23 + 3.64 = 26.64[/tex]
The 99% confidence interval for the population mean is (19.36, 26.64).
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ1
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
