Suppose medical researchers think that p = .70 is the proportion of all teenagers with high blood pressure whose blood pressure would decrease if they took calcium supplements. To test this theory, the researchers plan a clinical trial (experiment) in which n = 200 teenagers with high blood pressure will take regular calcium supplements.
a. Assume that p = .70 actually is the population proportion that would experience a decrease in blood pressure. What are the numerical values of the mean and standard deviation of the sampling distribution of P^, the sample proportion, for samples of n = 200 teenagers?
b. Use the results of part (a) to calculate an interval that will contain the sample proportion P^ for about 99.7% of all samples of n = 200 teenagers.
c. In the clinical trial, 120 of the 200 teenagers taking calcium supplements experienced a decrease in blood pressure. What is the value of P^ for this sample? Is this value a parameter or a statistic?
d. Given the answers for parts (b) and (c), explain why the observed value of P^ could be used as evidence that the researchers might be wrong to think that p = .70.