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 =

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