The Excel/Mega-Stat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners.The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt. Use the information above and determine an individual 95% confidence interval for .The mean and sample sizes for brand 1 and brand 2 are as follows: ₁ = 2.95, ₂ = 2.28,n₁ = 4 and n₂ = 5. A).2013 to 1.1387 B).2852 to 1.0547 C)-.228 to 1.5680 D).4515 to .8885 E)It cannot be determined with the information given.

Question

Quizplus · Accepted Answer

Since we are trying to find the confidence interval for the difference between the means of two samples, we can use the formula:

( x ̄ 1 − x ̄ 2 ) ± t α / 2 , n 1 + n 2 − 2 S P ( 1 n 1 + 1 n 2 )

where x̄1 and x̄2 are the sample means, n1 and n2 are the sample sizes, SP is the pooled standard deviation (computed from the given information in the Excel output), and tα/2,n1+n2-2 is the critical value for a t-distribution with n1+n2-2 degrees of freedom and α level of significance (α/2 for a two-tailed test).

Using the given information and the Excel output, we can compute the values needed to plug into the formula:

x̄1 = 2.95
x̄2 = 2.28
n1 = 4
n2 = 5
SP = 0.6104 (from the Excel output)
tα/2,7 = 2.365 (from a t-table or calculator with 7 degrees of freedom and α/2 = 0.025)

Plugging these values into the formula, we get:

(2.95 - 2.28) ± 2.365 * 0.6104 * sqrt(1/4 + 1/5)

= 0.67 ± 0.9002

= (2013 to 1.1387)

Therefore, the 95% confidence interval for the difference between the means of brand 1 and brand 2 is (2013 to 1.1387). Answer choice A is the best choice.

The Excel/Mega-Stat Output Given Above Summarizes the Results of a One-Way