Consider the following two questions designed to assess quantitertive literac 1,
ID: 3313630 • Letter: C
Question
Consider the following two questions designed to assess quantitertive literac 1, what s 15% of 1C00? Suppoac the 1st question asked 0 200 random y sekcted colle c students, with 153 ans cring oor ectly: the second o 2 is asked of a different random sample 202 collage stucents, rcsult ng n 142 corract responses Carry o ttest o hypothesc at sign car ce leve U US to dccide if he true roportion of co rect responses to the quest on without cortest exceeos that or the ore sth oontext Use o: or the trie prooort on studerts who sns e ec the question without context correct y d O2 for the ru proDorton of students who sns ered the quest on with Stete the relevent-ypotheses. Calcu ate t test tatistic 5nd p.value·(Round ycur test statstic to tao decrmal lases a d your fuelue to four dear!! paces.) P-valuc conclus on in tna prolem context. Fail to rejet M. The dats does not sugges that the true propertin of correct answers to the cortext-free questian is h gher than the proportion of right nzwers to the contextal cre Reject no. T·date suggests thst the true proportion of oorectenswers to the context-free question is h gher than the proportion ef right enswers to the " textuel cre. Fail to reject Ma The deta 8uggests the true proportion of correct enswers to the ontec free q estien is higher thon the progart on of right 8ns ers to the to textual cre. State thExplanation / 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: Option C is correct.
z = 2.47
P - value = 0.0068
Conclusion: Option B is correct.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 163 200 142 200 0.105 0.042555111 2.4673887 0.0068