Question

Hi, can you help me answer this question please, thank you

Answer 1

SOLUTION

Write out the given parameters in the questions

$\begin{gathered} \text{standard deviation =0.4 } \\ \text{sample ,n=20} \end{gathered}$

The critical value is the measurement used to calculate the margin of error within a set of data and is expressed as

$\begin{gathered} \text{Critical value =}1-\frac{\alpha}{2} \\ \text{where } \\ \alpha=0.05 \end{gathered}$

Then

$\text{critical value is the z=1.960}$

Therefore the critical value is1.960

Then the standard error is given by

$\begin{gathered} \sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}} \\ \\ \text{where } \\ n=\text{sample space=20 and }\sigma=0.4 \end{gathered}$

Substituting the value we have

$\sigma_{\bar{x}}=\frac{0.4}{\sqrt[]{20}}=\frac{0.4}{4.47}=0.089$

Therefore the standard error is 0.089

The confidence interval is given by

$\begin{gathered} \text{Confidence interval=}\bar{x}\pm(1.96)(S.E) \\ \text{where S.E= standard error } \end{gathered}$

The mean for the sample will be

$\bar{x}=\frac{sum\text{ of data}}{n}=\frac{3497.76}{20}=173.988$

Substitute the value to obtain the confidence interval

$\begin{gathered} \text{confidence interval=173.988}\pm1.96\times0.089 \\ C.I=173.988\pm0.174 \\ C\mathrm{}I=(173.814,174.162) \end{gathered}$

Therefore, the confidence interval is (173.81,174.16) to 2d.p