Question: Suppose that a study is designed to choose between the following hypotheses:
- Null hypothesis: Population proportion is .20.
- Alternative hypothesis: Population proportion is higher than .20.
- On the basis of a random sample of size 400, the sample proportion is .25.
a. Compute the z-score corresponding to the sample proportion of .25, assuming the null hypothesis is true.
b. What is the p-value for the standardized score computed in part (a)?
c. On the basis of the result from part (b), form a conclusion. Be explicit about the wording of your conclusion and justify your answer. Indicate the a that you chose to use.
d. Suppose that the sample size had only been 100, rather than 400, but the sample proportion was again .25. Using this smaller sample size, repeat parts (a) to (c).
e. Explain what this problem illustrates about the effect of sample size on statistical significance.