Question

Assume the population mean is to be estimated from the sample described. Use the sample results to approximate the margin of error and 95% coincidence interval N=36,x= 59.9seconds ,s=4.3 seconds I know the margin of error is 1.4 seconds. But how do I find the 95% coincidence interval?

Answer 1

At 95% confidence interval, we evaluate the critival value which is evaluated to be

`1.96`

The margin of error is expressed as

`\text{Margin of error = Z}*\frac{s}{\sqrt[]{N}}`

thus, we have

`\begin{gathered} \text{Margin of error = 1.96}*\frac{4.3}{\sqrt[]{36}} \\ =(1.96*4.3)/(6) \\ =1.4 \end{gathered}`

The confidence interval is expressed as

`CI\text{ = }\bar{x}\pm margin\text{ of error}`

thus, we have

`\begin{gathered} CI\text{ = 59.9}\pm1.4 \\ \end{gathered}`

Hence, the confidence interval is between 58.5 and 61.3.