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Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a standard deviation of $0.23. Construct a 95% confidence interval to estimate the population mean.

User Umberto
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Answer: ($3.055, $3.205)

Explanation:

Given : Significance level :
\alpha: 1-0.95=0.5

Critical value :
z_(\alpha/2)=1.96

Sample size : n= 36

Sample mean :
\overline{x}=\$\ 3.13

Standard deviation :
\sigma= \$\ 0.23

The confidence interval for population mean is given by :_


\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))


\text{i.e. }\$\ 3.13\pm (1.96)(0.23)/(√(36))\\\\\approx\$\ 3.13\pm0.075\\\\=(\$\ 3.13-0.075,\$\ 3.13+0.075)=(\$\ 3.055,\$\ 3.205)

Hence, the 95% confidence interval to estimate the population mean = ($3.055, $3.205)

User Jacek Francuz
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