Educators are interested in knowing whether a new experiment

Educators are interested in knowing whether a new experimental program has an impact on the reading readiness of first graders. Assume that with the existing program the mean Reading Readiness Score for all first graders is 100. A random sample of 41 first graders who have been through the new program had a mean score of 104 and a standard deviation of 24.5.

a. Draw and label a graph of the sampling distribution of xbar, a mean score for a random sample of 41 first graders under the existing program. (Since n=41 is fairly large, the central limit theorem applies, so you know the shape that the sampling distribution of xbar will have.) Use the sample s.d. s= 24.5 in place of the unknown population s.d.

b. Mark the location of xbar = 104 on your graph and shade in the region corresponding to the p-value of a test of H0: m=100 vs. Ha: m> 100, where m is the mean reading readiness score that would be achieved if ALL first graders used the new experimental program.

c. Based only on your sketch, does there appear to be statistically significant evidence that the new program is better than the existing one? Explain briefly.

d. Determine the p-value using your calculator or approximate it using the t-table, and see whether the improvement in mean score for the sample group is statistically significant at level a= 5%.

Solution