Mathematics: Arandom sample of 64 items is selected from a population of 400 items. the sample mean is 200. the population standard deviation is 48. from this data, a 95% confidence interval to estimate the population mean can be computed as

Arandom sample of 64 items is selected from a population

tgentryb60

02.01.2022

$(188.24,\ 211.76 )$ .

Step-by-step explanation:

Given : Sample size : n= 64 , the sample is a large sample (n>30), so we can apply z-test.

Sample mean = $\overline{x}=200$

Standard deviation : $\sigma=48$

Level of confidence: $1-\alpha=0.95$

$\Rightarrow\ \alpha=0.05$

Then, critical z-value = $z_{\alpha/2}=1.96$

The confidence interval to estimate the population mean is given by :_

$\overline{x}\ \pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$=200\ \pm\ (1.96)\dfrac{48}{\sqrt{64}}\\\\=200\pm11.76=(200-11.76, 200+11.76)=(188.24,\ 211.76 )$

Hence, the 95% confidence interval to estimate the population mean can be computed as $(188.24,\ 211.76 )$ .

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AHSYEDAN

30.06.2020

The measurement of angle S equals the measurement of angle R.

m∠S=m∠R

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