# Chapter 11: Comparisions of Means and Proportions

1. A statistics instructor is concerned that after her students perform well on the first of two major examinations in the introductory-level class, their performance appears to drop off on the second. Since this pattern appears to repeat itself across many sections of the same statistics class at her university, she wants to confirm that the downward trend in performance on the two 100-point examinations is real. To this end, she collects the examination results for a random sample of *n *= 12 students from the previous academic year. The scores on Exam 1 are: 79, 92, 81, 80, 79, 80, 78, 88, 86, 88, 77, and 93. On Exam 2, they are: 80, 75, 67, 82, 76, 71, 78, 78, 80, 77, 78, and 75. Create a data frame that organizes this data into two variables and 12 observations and use R to answer questions (b) and (c).

2. A recent study of the cost of living in various US cities has found regional differences in home prices. Two of the cities considered are Dallas, Texas and Minneapolis, Minnesota. The following data have been collected in the studies for those two cities: 47 homes in Dallas are for sale for an average of $151, 800, with a standard deviation of $17, 457; 34 comparable homes are for sale in Minneapolis for an average

of $207, 100, with a standard deviation of $26, 510.

3. The data set temps can be found on the book website. The two variable names are Daytemp and Nighttemp, and report the high (Daytemp) and low (Nighttemp) temperature in degrees Celsius for 10 European cities. The data are displayed below. Use R to answer parts (b) and (c).

temps

## City Daytemp Nighttemp

## 1 Athens 21 12

## 2 Barcelona 12 9

## 3 Dublin 6 1

## 4 Lisbon 15 9

## 5 Luxembourg 3 -2

## 6 Moscow 2 1

## 7 Munich 4 -2

## 8 Naples 14 11

## 9 Paris 7 -1

## 10 Stockholm 2 -4

5. In a recent consumer confidence survey of 400 adults, 54 of 200 men and 36 of 200 women expressed agreement with the statement, "I would have trouble paying an unexpected bill of $1, 000 without borrowing from someone or selling something." Do men and women differ on their answer to this question? Use the six-step framework to test *H*_{0} : *p*_{1} – *p*_{2} = 0 against *H*_{a} : *p*_{1} – *p*_{2} ≠ 0 at the* α* = 0.05 level of significance. What is the *p*-value? Use R to confirm your answers.