Question

Construct the confidence interval for the population mean μ.c=0.90, x=6.8, o = 0.7, and n = 43A 90% confidence interval for μ is (_,_) (Round to two decimal places as needed.)

Answer 1

Step-by-step explanation:

The given values in the question are

`\begin{gathered} CL=0.90 \\ \end{gathered}`

We will forst of all calculate the margin of error using the formula below

`\begin{gathered} E=z_{(\alpha)/(2)}(\sigma)/(√(n)) \\ where, \\ \sigma=0.7 \\ n=43 \\ z_{(\alpha)/(2)}=1.645(using\text{ z-score tbles for 90\% confidence interval\rparen} \end{gathered}`

Hence,

The margin of erro will be

`\begin{gathered} E=z_{(\alpha)/(2)}(\sigma)/(n) \\ E=1.645*(0.7)/(√(43)) \\ E=0.1756 \end{gathered}`

Hence,

The lower limit and upper limit will be calculated using the formula below

`\begin{gathered} lowerlimit=\bar{x}-E \\ Upperl\imaginaryI m\imaginaryI t=\bar{x}+E \\ where,\bar{x}=6.8 \end{gathered}`

By substituitng the values, we will have

`\begin{gathered} lowerl\imaginaryI m\imaginaryI t=\bar{x}-E=6.8-0.1756=6.6244 \\ Upperl\imaginaryI m\imaginaryI t=\bar{x}+E=6.8+0.1756=6.9756 \end{gathered}`

Hence,

The final answers to to decimal places is given below as

`(6.62,6.98)`