Question

A study comparing children’s reading age (in months) was developed using identical twin toddlers. One set of 6 twins played for 2 hours each day with educational toys (experimental group), the corresponding set of 6 twins played for 2 hours each day with non-educational toys (control group). The mean difference in reading age between the experimental group and control group of 6 sets of twins was -2.33 months and the standard deviation of the sample difference was 2.16 months. Set up a hypothesis test to determine if there is a difference between the 2 groups and use the appropriate sample test statistic to determine if the difference in reading age is significant at the 5% level..

Answer 1

H0: Null Hypothesis: ( there is no difference between the 2 groups)

HA: Alternative Hypothesis: ( there is a difference between the 2 groups) (claim)

n = Sample Size = 6

= The mean difference in reading age between the experimental group and control group of 6 sets of twins = 2.33

s_d = the standard deviation of the sample difference = 2.16

Test Statistic is given by:

= 0.05

df = 6 - 1 = 5

From Table, critical values of t = 2.5706

Since calculated value of t = - 2.6423 is less than critical value of t = - 2.5706, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a difference between the 2 groups.