In: Statistics and Probability
Consider the following two questions designed to assess quantitative literacy.
Suppose the first question is asked of 200 randomly selected college students, with 168 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 147 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.)
State the relevant hypotheses.
H0: p1 −
p2 = 0
Ha: p1 −
p2 < 0H0:
p1 − p2 = 0
Ha: p1 −
p2 ≠
0 H0:
p1 − p2 = 0
Ha: p1 −
p2 > 0H0:
p1 − p2 < 0
Ha: p1 −
p2 = 0H0:
p1 − p2 > 0
Ha: p1 −
p2 = 0
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z=P-value=
State the conclusion in the problem context.
Fail to reject H0. The data does not suggest that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data does not suggest the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one. Fail to reject H0. The data suggests the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.
You may need to use the appropriate table in the Appendix of Tables to answer this question.
We are allowed to do only 1 question at a time. Post again for
other answers.
2)
Reject H0. The data suggests that the true proportion of correct answers to the context-free question is higher than the proportion of right answers to the contextual one.