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Sagot :
Using the t-distribution, the 95% confidence interval of the population mean rating for Miami is (4.97, 6.51).
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 parameters for this problem are given as follows:
[tex]\overline{x} = 5.74, s = 2.7, n = 50[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Hence the bounds of the interval are given as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 5.74 - 2.0096\frac{2.7}{\sqrt{50}} = 4.97[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 5.74 + 2.0096\frac{2.7}{\sqrt{50}} = 6.51[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
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