1. 1. For a hypothesis test of H 0 :p 1 − p 2 = 0 against the alternative H a :p 1 − p 2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding? ...

1. 1. For a hypothesis test of H₀:p₁− p₂= 0 against the alternative H_a:p₁− p₂≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

a. The result is significant at both α = 0.05 and α = 0.01.

b. The result is significant at α = 0.05 but not at α = 0.01.

c. The result is significant at α = 0.01 but not at α = 0.05.

d. The result is not significant at either α = 0.05 or α = 0.01.

e. The result is inconclusive because we don't know the value of p.

2. At a large university, 20% of a random sample of male students have an overall grade point average (GPA) of 3.5 or higher. A random sample of female student records found that 25% had a GPA of 3.5 or higher. The president of the university wants to determine whether there is evidence of a difference in grades between males and females. What would she write as the null and alternative hypotheses for this situation?

a. H₀:p₁− p₂= 0 and H_a:p₁− p₂≠ 0

b. H₀:p₁− p₂= 0 and H_a:p₁− p₂> 0

c. H₀:p₁− p₂= 0 and H_a:p₁− p₂

d. H₀:p₁− p₂> 0 and H_a:p₁− p₂= 0

e. H₀:p₁− p₂> 0 and H_a:p₁− p₂≠ 0

3. A new technical cooking class compared 4,200 students who had not taken the class with 3,275 students who did. Of those students who did not take the cooking class, 2,760 increased their scores on the chef's examination compared to 2,135 who did take the class. A significance test was conducted to determine whether there is evidence that the students who took the cooking class were more likely to increase their scores on the chef's exam. What is the p-value for an appropriate hypothesis test?

a. 0.3184

b. 0.6367

c. 0.6816

d. 0

e. 1

4. Which of the following conditions must be met to conduct a two-proportion significance test?

I. The populations are independent.

II. The probabilities of success multiplied by the sample sizes are greater than 10 and the probabilities of failure multiplied by the sample sizes are greater than 10 for each population.

III. Each sample is a simple random sample.

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III