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g100num [7]
2 years ago
15

A safety auditor at a paint factory took a random sample of 25 cans of paint from a production run of over

Mathematics
2 answers:
stepan [7]2 years ago
7 0

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval is (29.6, 44.4).

<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 <u>two-tailed 95% confidence interval</u>, with 25 - 1 = <em>24 df</em>, is t = 2.0639.

The other parameters are given by:

\overline{x} = 37, s = 18, n = 25.

Hence, the bounds of the interval are given as follows:

\overline{x} - t\frac{s}{\sqrt{n}} = 37 - 2.0639\frac{18}{5} = 29.6

\overline{x} + t\frac{s}{\sqrt{n}} = 37 + 2.0639\frac{18}{5} = 44.4

The 95% confidence interval is (29.6, 44.4).

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

sammy [17]2 years ago
4 0

Answer:

<em>To simplify what the other person said:</em>

(29.57, 44.43)

Step-by-step explanation:

Proof that this is right on Khan

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