Question

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.

Answer 1

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)