Question

asked Sep 20, 2021 67.0k views

2 Answers

Tuukka Haapaniemi · Answer 1 · 2021-09-20T20:44:42+0000

The error bound (EBM) for the confidence interval with a 98% confidence level is approximately $59.88.

The error bound (EBM) for a confidence interval in a normal distribution is given by the formula:

EBM =
$Z * (\sigma)/(√(n))$

For a 98% confidence interval in a normal distribution, the Z-score is approximately 2.33.

Now, plug these values into the formula:

EBM =
2.33 * (158)/(√(23))

Calculating this, you get the error bound (EBM):

EBM
$\approx 2.33 * (158)/(√(23)) \approx 59.88 \]$

Therefore, the error bound (EBM) for the confidence interval with a 98% confidence level is approximately $59.88.

Konstantino Sparakis · Answer 2 · 2021-09-25T11:51:58+0000

Answer:

The 98% confidence interval is
$1713.23 <   \mu  <  1866.76$

Explanation:

From the question we are told that

The population standard deviation is
$\sigma = 158$

The sample size is n = 23

The sample mean is
$\= x = 1790 \ dollars$

From the question we are told the confidence level is 98% , hence the level of significance is

$\alpha = (100 - 98 ) \%$

=>
$\alpha = 0.02$

Generally from the normal distribution table the critical value of
$(\alpha )/(2)$ is

$Z_{(\alpha )/(2) } =  2.33$

Generally the margin of error is mathematically represented as

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

E = 2.33 * (158 )/(√(23) )

E =76.76

Generally 98% confidence interval is mathematically represented as

$\= x  -E <   \mu  <  \= x  +E$

$1790  -76.76 <  \mu  <  1790  +76.76$

$1713.23 <   \mu  <  1866.76$

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