A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities.In an effort to determine whether differences exist between the average fill rates for the two lines,a random sample of 19 bags from line 1 and a random sample of 23 bags from line 2 were recently selected.Each bag's weight was measured and the following summary measures from the samples are reported: Management believes that the fill rates of the two lines are normally distributed with equal variances.
Develop a 95% confidence interval estimate of the true mean difference between the two lines.

Question

A pet food producer manufactures and then fills 25-pound bags of dog food on two different production lines located in separate cities.In an effort to determine whether differences exist between the average fill rates for the two lines,a random sample of 19 bags from line 1 and a random sample of 23 bags from line 2 were recently selected.Each bag's weight was measured and the following summary measures from the samples are reported:

Management believes that the fill rates of the two lines are normally distributed with equal variances.
Develop a 95% confidence interval estimate of the true mean difference between the two lines.

Quizplus · Accepted Answer

We will use the two-sample t-interval formula: ( x1 − x2 ) ± tα/2 (Sp √(1/n1 + 1/n2)) where: x1 = sample mean of line 1 = 24.1684 x2 = sample mean of line 2 = 24.2660 n1 = sample size of line 1 = 19 n2 = sample size of line 2 = 23 Sp = pooled standard deviation = √(( (n1-1)S1^2 + (n2-1)S2^2 ) / (n1+n2-2)) = √(((18)(0.0144)+(22)(0.0184))/(19+23-2)) = 0.1104 α = significance level = 0.05/2 (since it's a two-tailed test) = 0.025 tα/2 = t0.025 with 40 degrees of freedom = 2.021 Substituting the given values: (24.1684 − 24.2660) ± 2.021(0.1104 √(1/19 + 1/23)) = -0.098 ≤ (µ₁ - µ₂) ≤ -0.002 Therefore, the 95% confidence interval estimate of the true mean difference between the two lines is -0.098 ≤ (µ₁ - µ₂) ≤ -0.002. The best choice is B.

A Pet Food Producer Manufactures and Then Fills 25-Pound Bags