Question

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample Size 50 18 10 17 Sample Mean 32 36 42 48The overall mean (the grand mean) for all treatments is: a. 37.3 b. 36.7 c. 48.3 d. 37.0

Answer 1

Answer:

Option (b) 36.7

Step-by-step explanation:

Data provided in the question:

                       Treatment 1     Treatment 2     Treatment 3      Treatment 4

Sample Size          50                   18                     10                          17

Sample Mean        32                   36                    42                         48

Now,

The overall mean is calculated as

= $\frac{\sum_{i = 1}^{4} n_i X_i}{\sum_{i = 1}^{4} {n_i}}$

Here, Xi = Sample mean

n = sample sizes

Thus,

Overall mean

= [ (50 × 32) + (18 × 36) + (10 × 42) + (17 × 48) ] ÷ [ 50 + 18 + 10 + 17 ]

= [ 1600 + 648 + 420 + 816 ]  ÷ 95

= 36.67 ≈ 36.7

hence,

Option (b) 36.7