Question

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

Answer 1

Given the following parameters

`\begin{gathered} \sigma\Rightarrow s\tan dard\text{ deviation=0.4} \\ n\Rightarrow\text{sample size=20} \\ \text{Significance level}\Rightarrow95\text{ \%} \\ z_{(\alpha)/(2)}=1.960 \end{gathered}`

To find the mean of the data, we will have to use

`\begin{gathered} \bar{x}=(\Sigma x_i)/(n) \\ \Sigma x_i=3497.76 \\ n=20 \\ \bar{x}=(3497.76)/(20) \\ =174.888 \end{gathered}`

Using the confidence interval formula of

`CI=\bar{x}\pm z_{(\alpha)/(2)}*\frac{\sigma}{\sqrt[]{n}}`

Substitute for all values to find the confidence interval.

`\begin{gathered} CI=174.888\pm1.960*\frac{0.4}{\sqrt[]{20}} \\ =174.888\pm1.960*0.0894427191 \\ =174.888\pm0.175 \end{gathered}`

Hence, the confidence interval is

`174.888\pm0.175`

The critical value is

`1.960`

The standard error of the mean is

`\sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}}=\frac{0.4}{\sqrt[]{20}}=0.089`

The confidence interval is

`(174.71,175.07)`