A certain dental condition which can be corrected if detected early enough occurs in the population with a frequency of p ¼ 0.20. An orthodontist believes that this condition occurs more frequently in children who were born with cleft palates and that parents of such children should be warned to watch for early evidence of the dental condition. To test his hypothesis, she follows the dental development of a random sample of 25 children born with cleft palates.
a. What is the most logical null hypothesis for the orthodontist to check? What alternative hypothesis should she use?
b. Suppose she wants a to be as close to 0.05 as possible; what region of rejection should she set for y, the number of children in the sample who develop this dental condition?
c. Suppose 8 of the children in her sample develop the condition. What is the P value? Should she reject the null hypothesis? Why, or why not? What conclusion should she draw?