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Assuming the population of interest is approximately normally​ distributed, construct a 95​% confidence interval estimate for the population mean given the values below. x overbar=19.3 s=3.1 n=23 The 95​% confidence interval for the population mean is from nothing to nothing.

1 Answer

1 vote

Answer:
(17.96,20.64)

Explanation:

The confidence interval for population mean is given by :-


\overline{x}\ \pm\ t_(n-1,\alpha/2)(s)/(√(n))

Given :
\overline{x}=19.3


s= 3.1

n=23, which is a small sample(n<30), so we use t-test.

Significance level:
1-0.95=0.05

Critical value :
t_(n-1,\alpha/2)=t_(22,0.025)=2.074

Then , the confidence interval for population mean will be :-


19.3\ \pm\ (2.074)(3.1)/(√(23))\\\\\approx19.3\pm1.34\\\\=(19.3-1.34,19.3+1.34)\\\\=(17.96,20.64)

Hence, the 95​% confidence interval for the population mean is
(17.96,20.64)

User Rob Sanders
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