Question

Question 1: A student at a university wants to determine if the proportion of students that use iPhones is less than 0.34. If the student conducts a hypothesis test, what will the null and alternative hypotheses be?

	1) HO: p < 0.34 HA: p ? 0.34
	2) HO: p > 0.34 HA: p ? 0.34
	3) HO: p = 0.34 HA: p ? 0.34
	4) HO: p ? 0.34 HA: p < 0.34
	5) HO: p ? 0.34 HA: p > 0.34

Question 2: A medical researcher wants to examine the relationship of the blood pressure of patients before and after a procedure. She takes a sample of people and measures their blood pressure before undergoing the procedure. Afterwards, she takes the same sample of people and measures their blood pressure again. The researcher wants to test if the blood pressure measurements after the procedure are different from the blood pressure measurements before the procedure. The hypotheses are as follows: Null Hypothesis: ?_D = 0, Alternative Hypothesis: ?_D ? 0. From her data, the researcher calculates a p-value of 0.678. What is the appropriate conclusion? The difference was calculated as (after - before).

	1) We did not find enough evidence to say there was a significantly negative average difference in blood pressure
	2) We did not find enough evidence to say the average difference in blood pressure was not 0.
	3) The average difference in blood pressure is significantly different from 0. The blood pressures of patients differ significantly before and after the procedure.
	4) The average difference in blood pressure is equal to 0.
	5) We did not find enough evidence to say there was a significantly positive average difference in blood pressure.

Question 3: Your friend tells you that the proportion of active Major League Baseball players who have a batting average greater than .300 is greater than 0.52, a claim you would like to test. The hypotheses for this test are Null Hypothesis: p ? 0.52, Alternative Hypothesis: p > 0.52. If you randomly sample 27 players and determine that 16 of them have a batting average higher than .300, what is the test statistic and p-value?

	1) Test Statistic: -0.755, P-Value: 0.225
	2) Test Statistic: -0.755, P-Value: 0.775
	3) Test Statistic: 0.755, P-Value: 0.45
	4) Test Statistic: 0.755, P-Value: 0.775
	5) Test Statistic: 0.755, P-Value: 0.225

Answer 1

1) Option - 4) H0 : P > 0.34

                      HA: P < 0.34

2) At 0.05 significance level, as the P-value is greater than the significance level (0.678 > 0.05), we should not reject H₀.

Option - 2) We did not find enough evidence to say the average difference in blood pressure was not 0.

3) p = 16/27 = 0.5926

The test statistic z = (p - P)/sqrt(P(1 - P)/n)

                             = (0.5926 - 0.52)/sqrt(0.52 * (1 - 0.52)/27)

                             = 0.755

P-value = P(Z > 0.755)

             = 1 - P(Z < 0.755)

             = 1 - 0.775

             = 0.225

Option - 5 is correct.