Question

A developmental psychologist believes that children raised in bilingual families will have higher verbal fluency at age 3 than children raised in families where only one language is spoken. She recruits 25 bilingual and 25 monolingual families with 3-year olds from her local newspaper and administers the Childhood Test of Verbal Fluency (CTVF) to each child. She finds that mean CTVF test score for bilingual children is 5 points higher than the mean CTVG score for monolingual children. She then performs a t-test on the null hypothesis: CTVFbilingual ≤ CTVFmonolingual at the α=.05 significance and finds an observed significance level of p=.15.

1. Did the researcher perform a one-tailed or two-tailed test?

2. How would you write the alternative hypothesis?

3. What statistical distribution was used to carry out the test?

4. Assume that bilingual 3-year olds really do have higher verbal fluency than monolingual 3-year olds. In other words, this difference is true in the population. What type of error did the research make?

Answer 1

(1) This is a one-tailed (upper tailed) test

(2) CTVFbilingual > CTVFmonolingual

(3) t- test for independent samples (so a t- distribution with 25 + 25 - 2 = 48 degrees of freedom was used since the sample sizes are < 30)

(4) Since the p- value for the test 0.15 > 0.05, the researcher will fail to reject the null hypothesis, while the alternative hypothesis is true. The researcher will make a type II error.