A bottling plant produces 1 liter bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ and standard deviation σ = 0.05 liter. We randomly select 6 bottles andmeasure the volume of soda in each. The results of these 6 measurements (all in liter units) are 1.05 1.04 1.01 1.06 0.94 0.99. Based on these data, a 90% confidence interval for μ is
Accepted Solution
A:
μ = population mean σ = 0.05, the population standard deviation
Because the sample size is less than 30, the confidence interval is [tex]\bar{x} \pm t^{*} \frac{\sigma}{ \sqrt{n} } [/tex] where t* = 2.015, fromm the t-distribution with dof = 6-1 = 5.
The confidence interval for μ is 1.015 +/- 2.015(0.05/√6) = 1.015 +/- 0.0411 = (0.974, 1.056)