Question

Picture Arrangement Scores

Left-Handed: 12, 10, 12, 14, 12, 10, 8.13,7

Right-Handed: 8, 10, 10, 12, 11, 6, 7,9,11

   •   Is there a significant difference in the Picture Arrangement scores between the right- and left-handed students? Use α = .05 in making your decision. Be sure to state your hypotheses in symbols and use subscripts to denote each group e.g., and to represent the true population mean Picture Arrangement score for right- and left-handed students, respectively. Include the following in your response, if necessary – test statistic, degrees of freedom, computations, critical value(s), and conclusion in the context of the problem.

   •   What is the 95% confidence interval for the difference between the means?

   •   What does it mean if a confidence interval for the true mean difference contains 0? In other words, does this provide evidence that there truly is a mean difference between the two groups or not?

Answer 1

Based on the given data:

Let denote the mean Picture Arrangement scores of the right and left-handed students respectively. We are asked to test,

Vs    at 5% level of significance.

The appropriate statistical tool to test the above hypothesis would be an Independent sample t test, with test statistic given by,

Assuming equal variances,

with rejection region

Substituting the values,

(Here, the observation in left handed student group is considered to be "8.13". * If incorrect, considering it to be two different observations 8 and 13, the test is re-run below.)

Sample means:

Sample Variances:

And Sample sizes n₁ = 9, n₂ = 8

We get,

t = - 1.25

Comparing the test statistic obtained with the critical value of t for alpha = 0.05 and for = 15 degrees of freedom, from t table,

We get t(0.05,9+8-2=15) = 2.131

Since, |t| = 1.25 < 2.131 does not lie in the critical region, we fail to reject H0 at 5% level. We may conclude that the data does not provide sufficient evidence to support the claim that there a significant difference in the Picture Arrangement scores between the right- and left-handed students.

Case 2: Considering the observations as 8 and 13:

Sample means:

Sample Variances:

And Sample sizes n₁ = n₂ = 9

We get,

t = -1.53

Comparing the test statistic obtained with the critical value of t for alpha = 0.05 and for = 16 degrees of freedom, from t table,

We get t(0.05,16) = 2.120

Since, |t| = 1.53 < 2.12 does not lie in the critical region, we fail to reject H0 at 5% level. We may conclude that the data does not provide sufficient evidence to support the claim that there a significant difference in the Picture Arrangement scores between the right- and left-handed students.