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Noam is interested in estimating the average age of the Summer Olympians who have competed since 1980. She randomly selected 24 Olympians, and the result was this list of ages: 16, 17, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 32 Construct and interpret a 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics. Use the table to determine the appropriate value of t*. Enter in the degrees of freedom and the value of t* (exactly as you see it written in the table). Degrees of freedom =

Sagot :

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.

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.

In this problem, with the help of a t-distribution calculator, with a two-tailed significance level of 0.02 and 24 - 1 = 23 degrees of freedom, the parameters are:

[tex]\overline{x} = 22.7, s = 4.15, n = 24, t = 2.5[/tex]

Then, the interval is:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 22.7 - 2.5\frac{4.15}{\sqrt{24}} = 20.6[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 22.7 + 2.5\frac{4.15}{\sqrt{24}} = 24.8[/tex]

The 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.

More can be learned about the t-distribution at https://brainly.com/question/16162795

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