Samples Were Drawn from Three Populations $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$

question 26

Short Answer

Samples were drawn from three populations. The sample sizes were n₁=8, n₂=8, and n₃=7 . The sample means were $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$ , and $\bar { x } _ { 3 }$ =2.57 . The sample standard deviations were s₁=0.27, s₂=0.45, and s₃=0.25 . The grand mean is =2.055217.
i). Compute the sums of squares SSTr and SSE.
ii). How many degrees of freedom are there for SSTr and SSE?
iii). Compute the sums of squares MSTr and MSE.
iv). Compute the value of the test statistic F.
v). Can you conclude that two or more of the population means are different? Use the $\alpha = 0.05$ level of
significance.

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Definitions:

Testicular Cancer

A type of cancer that develops in the testicles, the male reproductive glands that produce sperm and testosterone.

Prostatitis

Inflammation of the prostate gland, often causing pelvic pain and difficulties with urination.

Benign Prostatic Hypertrophy

A noncancerous enlargement of the prostate gland.

Benign Prostatic Hypertrophy

A noncancerous enlargement of the prostate gland, common in older men, which can lead to urinary problems.