Statistics Test 2 - Spring 2008, Exams of Statistics

A statistics test from math 140e, held in spring 2008. The test covers various statistical concepts such as correlation coefficients, standard deviations, regression analysis, percentiles, and probability. Students are required to find correlation coefficients, standard deviations, regression lines, and estimates based on given data.

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Pre 2010

Uploaded on 08/18/2009

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Math 140E: Test #2 Spring 2008 Page 1 of 6
Your Name: _____________________ ____
Math 140: Statistics
Test 2, March 27, 2008
1. (8 pts.) The correlation coefficient for the first table is 0.7857. Give the correlation
coefficient for each of the remaining tables. You should use either the given
correlation coefficient or your knowledge of correlation coefficients to find these
without doing any real calculations.
x
y
1
2
2
3
3
1
4
4
5
6
6
5
7
7
x1
y1
1
–4
2
–6
3
–2
4
–8
5
–12
6
–10
7
–14
x2
y2
1
6
2
7
3
5
4
8
5
10
6
9
7
11
x3
y3
3
1
4
2
2
3
5
4
7
5
6
6
8
7
x4
y4
1
–1
2
–2
3
–3
4
–4
5
–5
6
–6
7
–7
a) x1 and y1
b) x2 and y2
c) x3 and y3
d) x4 and y4
2. (6 pts.) Find the standard deviation for each of the following sets of data using the
short-cut method presented in Chapter 17:
a) –1, –1, –1, 5, 5, 5
b) 0, 0, 0, 0, 5
pf3
pf4
pf5

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Your Name: _________________________ Math 140: Statistics Test 2, March 27, 2008

  1. (8 pts.) The correlation coefficient for the first table is 0.7857. Give the correlation coefficient for each of the remaining tables. You should use either the given correlation coefficient or your knowledge of correlation coefficients to find these without doing any real calculations. x y 1 2 2 3 3 1 4 4 5 6 6 5 7 7 x1 y 1 – 4 2 – 6 3 – 2 4 – 8 5 – 12 6 – 10 7 – 14 x2 y 1 6 2 7 3 5 4 8 5 10 6 9 7 11 x3 y 3 1 4 2 2 3 5 4 7 5 6 6 8 7 x4 y 1 – 1 2 – 2 3 – 3 4 – 4 5 – 5 6 – 6 7 – 7 a) x1 and y b) x2 and y c) x3 and y d) x4 and y
  2. (6 pts.) Find the standard deviation for each of the following sets of data using the short-cut method presented in Chapter 17: a) – 1, – 1, – 1, 5, 5, 5 b) 0, 0, 0, 0, 5
  1. (16 pts.) A hypothetical study of working couples yielded the following results:. Husband’s Income: Average = $54,000, SD = $39, Wife’s Income: Average = $33,000, SD = $26,000, r=0. a) When estimating the wife’ income from the husband’s, what is the slope of the regression line? b) What is the intercept of the regression line? c) Write the equation of the regression line. d) If a husband makes $75,000, use the regression line to estimate his wife’s income. Show your work!
  2. (6 pts.) Using the data from the previous problem and the regression technique , estimate the income of a husband whose wife earns $72,000.
  1. (12 pts.) In a hypothetical study, the following results were obtained: Father’s Weight at 21: Average = 182, SD = 12 Son’s Weight at 21: Average = 188, SD = 15, r = 0. a) What percentage of the fathers weigh over 200 pounds? b) For the father’s that weigh 200 pounds, what percentage of their sons weigh over 200 pounds?
  2. (6 pts.) A fair coin is flipped repeatedly. a) You win a dollar if there are between 40% and 60% heads. Which is better: 10 flips or 100 flips? b) You win a dollar if there are more that 60% heads. Which is better: 10 flips or 100 flips? c) You win a dollar if there are exactly 50% heads. Which is better: 10 flips or 100 flips?
  1. (8 pts.) Give a box model based on a standard deck of 52 cards for each of the following: a) You win $3 if you draw a red face card and you lose $1 if you draw any other card. b) You win $2 for a face card, win $1 for a nine or ten, and lose $1 for any other card.
  2. (8 pts.) If 400 draws with replacement are made from the box: 0 2 4 4 6 what is the chance of getting between 70 and 90 sixes?