Respuesta :
Using the t-distribution, the 90% confidence interval for the population mean is given by:
(509.25, 519.23).
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 90% confidence interval, with 87 - 1 = 86 df, is t = 1.6628.
Researching this problem on the internet, the parameters are given by:
[tex]\overline{x} = 514.24, s = 28, n = 87[/tex]
Hence the bounds of the interval are given by:
- [tex]\overline{x} - t\frac{s}{\sqrt{n}} = 514.24 - 1.6628\frac{28}{\sqrt{87}} = 509.25[/tex]
- [tex]\overline{x} + t\frac{s}{\sqrt{n}} = 514.24 + 1.6628\frac{28}{\sqrt{87}} = 519.23[/tex]
The 90% confidence interval for the population mean is given by:
(509.25, 519.23).
More can be learned about the t-distribution at https://brainly.com/question/16162795
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