Question

2. A groups of developmental psychologists wanted to examine under what conditions children of 24 month of age can generate the most number of words. They randomly selected 45 children and randomly assigned them to three different conditions. Then they measured the number of words the children uttered in the three conditions. Specify the null hypothesis and test it at the significance level of .05. What is your conclusion? Make sure to provide the summary table from SPSS. Child playing alone After bath After dinner 21 47 39 2 19 42 6 24 10 1 12 24 7 48 29 53 53 34 0 20 45 6 17 31 10 29 35 18 41 65 9 67 55 23 38 57 25 51 98 2 31 43 24 58 75

Answer 1

Solution:-

Anova: Single Factor SUMMARY Groups Count Sum Average Variance 13.8 197.0286 37 281.2857 682 45.46667 481.2667 Playing alone After bath Afiirir 207 15 15 15 ANOVA Source of VariationSS Between Groups Within Groups df P-value F crit MS 8063.511 13434.13 2 4031.756 12.60474 5.15-053.219942 42 319.8603 Total 21497.64

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

MSB MSE

F = 12.605

F_critical = 3.22

Interpret results. Since the F-value (12.605) lies in the rejection region, hence we have to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the number of words the children uttered in the three conditions.