Sentence complexity study. Refer to the Applied Psycholinguistics (June 1998) study of language skills of low-income children, presented in Exercise. Each in a sample of 65 low-income children was administered the Communicative Development Inventory (CDI) exam. The sentence complexity scores had a mean of 7.62 and a standard deviation of 8.91.
a. Construct a 90% confidence interval for the mean sentence complexity score of all low-income children.
b. Interpret the interval you found in part a in the words of the problem.
c. Suppose we know that the true mean sentence complexity score of middle-income children is 15.55. Is there evidence that the true mean for low-income children differs from 15.55? Explain.
Sentence complexity study. A study published in Applied Psycholinguistics (June 1998) compared the language skills of young children (16–30 months old) from low-income and middle-income families. A total of 260 children—65 in the low-income and 195 in the middle-income group—completed the Communicative Development Inventory (CDI) exam. One of the variables measured on each child was sentence complexity score. Summary statistics for the scores of the two groups are reproduced in the accompanying table. Use this information to sketch a graph of the sentence complexity score distribution for each income group. (Assume that the distributions are mound shaped and symmetric.) Compare the distributions. What can you infer?
| Low Income | Middle Income |
Sample Size | 65 | 195 |
Mean | 7.62 | 15.55 |
Standard Deviation | 8.91 | 12.24 |
Minimum | 0 | 0 |
Miximum | 36 | 37 |
Based on Arriaga, R. I., et al. “Scores on the MacArthur Communicative Development Inventory of children from low-income and middleincome families.” Applied Psycholinguistics, Vol. 19, No. 2, June 1998, p. 217 (Table).
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