Question

Twenty-seven participants (9 per group) were randomly assigned to do a series of math tasks while listening to sof. gentle music, while listening to loud-intense music, or while in silence. The means and estimated population variances for the three groups were: Soft-Gentle: M-37, s 32; Loud-Intense: M- 33, S 28; Silence: M-41, 30. Using the 05 significance level, is there a difference in performance on this kind of math task under these three conditions? Step I. Restatethe research Question. 23 Identify the population(s): (i) (ii) Research hypothesis: (iii) Null hypothesis: Step 2: Give the characteristics (including the degrees of freedom) of the comparison distribution Step 3: Determine the cut-off or critical value from the table Step 4: Determine the appropriate statistic using the steps below (0) Compute the between-group estimate of variance Compute the within-group estimate of variance. (ii) Page 7 of 1

Answer 1

Solution

Step 1

Part (i)

Population: Set from which the 27 participants were selected. Answer 1

Part (ii)

Research hypothesis: Performance in math task can be influenced by the type of music listened to while performing the task. Answer 2

Part (iii)

Null hypothesis: H₀: Mean performance is the same under the three conditions. Answer 3

Step 2

Distribution is F with degrees of freedom, 2 and 24. Answer 4

[First df is the df for between conditions which is 1 less than the number of conditions; the second is df for error which is total df – between df. Total df = total number of observations – 1]

Step 3

Given 0.05 as the significance level, critical value =F_{2, 24, 0.05}, i.e., upper 5% point of F with degrees of freedom, 2 and 24 = 3.40 Answer 5

Step 4

Part (i)

Between group estimate of variance = (1/2)Σ(x_i.bar – x_..bar)² where x_..bar = (37 + 33 + 41)/3 = 37

= (1/2){(37 – 37)² + (33 – 37)² +(41 – 37)²}

= 16 Answer 6

Part (ii)

Within group estimate of variance = (1/3)ΣS_i²

= (32 + 28 + 30)/3

= 30   Answer 7

Part (iii)

Test statistic: F = Between group estimate of variance/Within group estimate of variance = 16/30

= 0.53333 Answer 8

DONE

[Going beyond,

Since F (0.5333) < Fcrit (3.40), null hypothesis is accepted and hence we conclude that the performance in math task is not influenced by the type of music listened to while performing the task.]