Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25 _overall = 39 ₁ = 33 ₂ = 43 ₃ = 49 ₄ = 31
Compute a 95% confidence interval for the first treatment mean.

Question

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25

_overall = 39 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25 overall = 39 1 = 33 2 = 43 3 = 49 4 = 31 Compute a 95% confidence interval for the first treatment mean. A) (12.75 53.25) B) (25.14 40.86) C) (23.46 42.54) D) (20.51 45.49)

₁ = 33

₂ = 43

₃ = 49

₄ = 31
Compute a 95% confidence interval for the first treatment mean.

Quizplus · Accepted Answer

First, we need to find the point estimate for the first treatment mean, which is _overall = 39. Next, we need to use the following formula to find the confidence interval: (point estimate) +/- (t-value) x (standard error) The standard error can be calculated as the square root of MSE divided by the number of observations in that treatment group. For the first treatment group, there are 5 observations, so the standard error is: sqrt(101.25/5) = 6.345 The t-value can be obtained from a t-distribution table with 4 degrees of freedom (i.e., 5-1). For a 95% confidence interval, the t-value is 2.776. Plugging in the values, we get: 39 +/- 2.776 x 6.345 This simplifies to: (23.46, 42.54) Therefore, the correct answer is C, (23.46, 42.54).

Consider the Following Calculations for a One-Way Analysis of Variance