Q1) In a confidence interval for a population proportion p, a decrease in which of the following quantities will definitely make the interval wider?

a. p

b. p(1 p)

c.n

d. both (a) and (c)

Which answer is correct and why?

Q2) Which of the following tests should always be one-sided?

a. the sign test

b. the single sample t-test for a mean

c. the contingency table test for independence

d. the t-test for a regression coefficient

Q3) A 95% confidence interval for a population proportion p is calculated, using p = 0.5 in the standard error. The sample proportion is not equal to 0.5. Which of the following statements is FALSE?

a.using p = 0.5 in the standard error ensures the interval's confidence level is at least 95%, irrespective of the true value of p

b.Using the sample proportion in the standard error will make the interval narrower

c.if the interval does not include p = 0.5, then recalculating the interval using the sample proportion in the standard error is appropriate

d.none of the above

Which one and why?