Consider the following two questions designed to assess quantitative literacy 1,
ID: 3313995 • Letter: C
Question
Consider the following two questions designed to assess quantitative literacy 1, what is 15% of 1000? 2, A store is offering a 15% off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 164 answering correctly; the second one is asked of a different random sample of 200 college students, resulting i 140 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. Hai P1-P2=0 Ha: p1-p2 = 0 Ha: P1 P20 0H0: 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.) P-value State the conclusion in the problem context Fail to reject Ho. 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. O Reject Ho. 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. O Reject Ho- 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 0 Fail to reject Ho-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 oneExplanation / Answer
The statistical software output for this problem is:
Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 > 0
Hypothesis test results:
Hence,
Hypotheses:
Ho: p1 - p2 = 0
Ha: p1 - p2 > 0
z = 2.81
p - Value = 0.0025
Conclusion: Option B is correct.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 164 200 140 200 0.12 0.042708313 2.8097574 0.0025