Get personalized and accurate responses to your questions with IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
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
#SPJ1
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.
