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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
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