Question

Please answer ALL questions on page:

1. Cognitive science consistently shows that one of the most effective studying tools is to self - test. A recent study reinforced this finding. In the study, 118 college students stu died 48 pairs of Swahili and English words. All students had an initial study time and then three blocks of practice time. During the practice time, half the students studied the words by reading them side by side, while the other half gave themselves qu izzes in which they were shown one word and had to recall its partner. Students were randomly assigned to the two groups, and total practice time was the same for both groups. On the final test one week later, the proportion of items correctly recalled w as 15% for the reading - study group and 42% for the self - quiz group. The standard error for the difference in proportions is about 0.07. Test whether giving self - quizzes is more effective and show all details of the test. The sample size is large enough to use the normal distribution.

2. Referring to the data set we used in Chapter 2 c omparing servers, tips, and credit card usage, we have the following two - way table showing the servers and whether or not the customer used a credit card to pay for their meal.

A B C

Yes 21 15 15

No 39 50 17

a) Compute and interpret a 95% confidence interval for the proportion of bills paid with a credit card.

b) Compute and interpret 90% confidence interval s for t he proportion of bills for each server.

c) From the confidence intervals in part b) does it appear that Server B is responsible for 1/3 of the bills this week?   

Answer 1

1) The hypothesis can be expressed as follows:

where p_q and p_r are the proportions of words recalled correctly after quiz studying or studying by reading alone, respectively.

Based on the given information, we get the statistic of interest as

The standard error of this statistic is given as SE = 0.07 and the null hypothesis is that the difference in the proportions for the two group is zero. We compute the standardized test statistic with

Using technology, the area under a N(0, 1) curve beyond z = 3.86 is only 0.000056. This very small p-value provides very strong evidence that the proportion of words recalled using self-quizzes is more than the proportion recalled with reading study alone.

2) For ques 2 I would need standard error value.