The lumen output was determined for each of

G = 3

different brands of lightbulbs having the same wattage, with J = 10 bulbs of each brand tested (this is the number of observations in each treatment group). The sums of squares were computed as SSG = 593.3 and SSE = 4776.9. State the hypotheses of interest (including word definitions of parameters).

μ_i = sample average lumen output for brand i bulbs
H₀: μ₁ = μ₂ = μ₃
H_a: all three μ_i's are unequal μ_i = true average lumen output for brand i bulbs
H₀: μ₁ = μ₂ = μ₃
H_a: at least two μ_i's are unequal μ_i = sample average lumen output for brand i bulbs
H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: all three μ_i's are equal μ_i = true average lumen output for brand i bulbs
H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: at least two μ_i's are equal

Use the Single Factor ANOVA F test with

(α = 0.05)

to decide whether there are any differences in true average lumen outputs among the three brands for this type of bulb.
Calculate the F test statistic then use R to find your p-value using the CDF of the f distribution pf().
Recall the p-value from an F test is always the area to the right of the F test statistic. Example: 1-pf(f test statistic, df1, df2)
f statistic = (Round your answer to two decimal places.)
p-value = (Round your answer to four places.)

State the conclusion in the problem context.

Fail to reject H₀. There are no statistically significant differences in the lumen output. Reject H₀. There are no statistically significant differences in the lumen output. Fail to reject H₀. There are statistically significant differences in the lumen output. Reject H₀. There are statistically significant differences in the lumen output.