1 Answer

Tspano · Answer 1 · 2021-12-12T14:30:07+0000

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is
$49.85 < \mu < 54.15$

This means that there is 95% chance that the true population mean is within this interval

Explanation:

From the question we are told that

The sample size is n = 30

The sample mean is
$\= x = 52$

The population standard deviation is
$\sigma = 6$

Given that the confidence level is 95% then the level of confidence is evaluate as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of
$(\alpha )/(2)$ from the normal distribution table , the values is

$Z_{(\alpha )/(2) } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * (\sigma )/(√(n) )$

substituting values

E = 1.96 * ( 6 )/(√(30) )

E = 2.147

The 95% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

substituting values

$52 - 2.147 < \mu < 52 + 2.147$

$49.85 < \mu < 54.15$

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