Question

1. One criticism of reading comprehension tests is that while they may measure reading comprehension, they also measure other factors not related to reading comprehension. A reading comprehension (RC) test on a major college entrance exam provides short English prose passages, and the examinees answer a set of multiple-choice items about the passage. To see if particular items measure something other than RC, investigators gave the RC test without the reading passages to a random sample of psychology students. The investigators reasoned that if questions were measuring knowledge or memory rather than just RC, students would answer questions at a higher rate than chance (20%, since there were 5 choices for each question.)

   Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this sufficient evidence that students are using more than just reading comprehension to answer this question? Test the relevant hypothesis using  = .05.

Answer 1

Null hypothesis Ho: p = 0.20

Alternate hypothesis Ha: p >0.20

population proportion po = 0.20

sample proportion p(hat) = 30/100 = 0.30

sample size n = 100

z test statistics =

using z distribution table, check 2.5 in the left most column and 0.00 in the top most row, select the intersecting cell, we get

p value = 0.0062

p value is less than significance level of 0.05, rejecting the null hypothesis

We can conclude that there is sufficient evidence to say that population proportion is higher than 20%