Question

Identify the following specifications:

a. lower limit

b. upper limit

c. error bound

Short answer

The lower limit is 24.52$the95\backslash \%confidenceintervalis24.52$

The upper limit is 36.28

The error bound is 5.88

Step-by-step solution

Given Information (a)

The sample mean is $30.4$, that is, $\overline{x}=30.4$

The confidence level is $95\%$, that is,$\alpha =0.05$

We have to find lower limit

Explanation of (b)

The lower limit is calculated using the formula given below,

Lower Limit$=\overline{x}-z_{\frac{a}{2}}\frac{\sigma }{\sqrt{n}}$

The calculation is given below,

Lower Limit $=\overline{x}-z_{0.025}\frac{\sigma }{\sqrt{n}}$

$=30.4-1.96\times \frac{15}{\sqrt{25}}$

$=30.4-1.96\times 3$

=24.52

Given Information of (b)

The sample mean is$30.4$, that is, $\overline{x}=30.4$.

The confidence level is $95\%$, that is,$\alpha =0.05$

We have to find upper bound

Calculation of upper bound

The upper limit calculation formula is given below

Upper bound=$\overline{x}+z_{\frac{a}{2}}\frac{\sigma }{\sqrt{n}}$$=\overline{x}+z_{\frac{a}{2}}\frac{\sigma }{\sqrt{n}}$

$=30.4+1.96\times \frac{15}{\sqrt{25}}$

$=30.4+1.96x3$

=36.28

Given Information of (c)

The sample mean is $30.4$, that is, $\overline{x}=30.4$.

The confidence level is $95\%$, that is, $\alpha =0.05$

We have to find the error bound

Calculation of Error Bound

The error bound is calculated using the formula given below,

$EBM=z_{\frac{a}{2}}\frac{\sigma }{\sqrt{n}}$

$EBM=z_{0.025}\frac{15}{\sqrt{25}}$

$=1.96\times \frac{15}{5}$

=5.88