Suppose a random sample of 100 observations from a binomial population gives a value of p̂ =.69 and you wish to test the null hypothesis that the population parameter p is equal to.75 against the alternative hypothesis that p is less than.75.
a. Noting that p̂ =.69, what does your intuition tell you? Does the value of p̂ appear to contradict the null hypothesis?
b. Use the large-sample z-test to test H0: p =.75 against the alternative hypothesis Ha: p<.75. Use p̂ =.05. How do the test results compare with your intuitive decision from part a?
c. Find and interpret the observed significance level of the test you conducted in part b.
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