Question

Here are summary statistics for randomly selected weights of newborn​ girls: n=185​,

x bar = 31.4 ​hg, s=7.5 hg. Construct a confidence interval estimate of the mean. Use a 95​% confidence level.


What is the confidence interval for the population mean μ​?

Answer 1

Answer:

The confidence  interval for the population mean μ​ is $32.487<\mu <30.313$

Step-by-step explanation:

Given :

Number of weights of newborn​ girls n=185.

Mean $\bar{x}=31.4$ hg

Standard deviation s=7.5 hg

Use a 95​% confidence level i.e. cl=0.95

To find : What is the confidence interval for the population mean μ​?

Solution :

Using t-distribution,

The degree of freedom $DF=n-1=185-1=184$

$\alpha=\frac{1-0.95}{2}$

$\alpha=0.025$

The t critical value is t=1.973.

The confidence interval build is

$CI=\bar{x}\pm(t\cdot \frac{s}{\sqrt{n}})$

Substitute the values,

$CI=31.4\pm(1.973\cdot \frac{7.5}{\sqrt{185}})$

$CI=31.4\pm(1.973\cdot 0.5514)$

$CI=31.4\pm(1.087)$

$31.4+1.087<\mu <31.4-1.087$

$32.487<\mu<30.313$

Therefore, the confidence  interval for the population mean μ​ is $32.487<\mu <30.313$