Research on reducing stuttering in preschool children between the ages of 3 to 6 looked at 199 children who were registered in one of 20 participating speech therapy clinics throughout the Netherlands. The children were randomly assigned to one of two treatment methods: direct treatment (the Lidcombe program, LP) or indirect treatment (the RESTART demands and capacities model). After 18 months of treatment, the proportions of non-stuttering children were compared. The number of children completing the study in the LP group was 85; in the RESTART group, 91 completed the study. 

a. Using words or appropriate symbols, state the hypotheses to be tested. 

b. In the LP group, 65/85 were classified as non-stuttering after 18 months in the study; in the same time period, 65/91 in the RESTART program were classified as non-stuttering. Using these d data, fill in a 2 × 2 table and calculate the observed proportions of non-stuttering children for each of the two treatment groups. 

c. Calculate the difference in the proportion of non-stuttering children for the LP group compared to the RESTART group. 

d. Use the Multiple Proportions applet to run the test of significance. Report the p-value 

e. Find the confidence interval for the difference in the proportion of non-stutterers (LP − RESTART) and draw conclusions including generalizing and cause-and-effect conclusions.