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bekas [8.4K]
2 years ago
11

A medical center conducted a study to investigate cholesterol levels in people who have had heart

Mathematics
1 answer:
Zinaida [17]2 years ago
6 0

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 90% confidence interval is (246.6, 282.8).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm t\frac{s}{\sqrt{n}}

In which:

  • \overline{x} 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 <u>90% confidence interval</u>, with 16 - 1 = 15 df, is t = 1.7531.

Researching the problem on the internet, the standard deviation was of 42.1 mg/dL, hence the parameters are as follows:

\overline{x} = 264.7, s = 41.2, n = 16

Thus, the bounds of the interval are given by:

\overline{x} - t\frac{s}{\sqrt{n}} = 264.7 - 1.7531\frac{41.2}{\sqrt{16}} = 246.6

\overline{x} + t\frac{s}{\sqrt{n}} = 264.7 + 1.7531\frac{41.2}{\sqrt{16}} = 282.8

The 90% confidence interval is (246.6, 282.8).

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

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