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Math 140E: Statistics Test #3, Exams of Statistics

Wofford CollegeStatistics

This is a test for math 140: statistics course at the university of california, irvine (uci) in spring 2008. It covers topics such as standard error, confidence intervals, hypothesis testing, and t-tests. The test has 10 questions, some of which require calculations based on a given scenario.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

koofers-user-dqs
koofers-user-dqs 🇺🇸

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Math 140E: Test #3 Spring 2008 Page 1 of 6
Your Name: _____________________ ____
Math 140: Statistics
Test 3, May 1, 2008
1. (4 pts) Match the formula in the first column with the description in the second. Put
your answer in the blank provided in the second column.
i)
!
numberDraws "SD
a) SE for Percent: _____
ii)
!
numberDraws "SD
numberDraws
b) Combined SE _____
iii)
!
numberDraws "SD
numberDraws "100
c) SE for Average: _____
iv)
!
1stSE 2+2ndSE 2
d) SE for Sum: _____
2. (4 pts.) This is from Figure 7 on page 321 of your text.
It is for the sum of fifty draws from the box:
a) The shaded area represents the probability the total will be between __________
and __________ exclusive.
b) On the above figure, carefully shade the area that represents the probability the
total will be between 105 and 110 inclusive.
3
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Your Name: _________________________ Math 140: Statistics Test 3, May 1, 2008

  1. (4 pts) Match the formula in the first column with the description in the second. Put your answer in the blank provided in the second column. i) ! numberDraws " SD a) SE for Percent: _____ ii) ! numberDraws " SD numberDraws b) Combined SE _____ iii) ! numberDraws " SD numberDraws " 100 c) SE for Average: _____ iv) ! 1 stSE 2
  • 2 ndSE (^2) d) SE for Sum: _____
  1. (4 pts.) This is from Figure 7 on page 321 of your text. It is for the sum of fifty draws from the box: a) The shaded area represents the probability the total will be between __________ and __________ exclusive. b) On the above figure, carefully shade the area that represents the probability the total will be between 105 and 110 inclusive.
  1. (12 pts.) According to a recent census, a hypothetical city with a population of 100,000 people age 18 or older, 20% have college degrees. A sample of 2500 people is drawn without replacement. a) Find the expected value and SE for the number of people in the sample with college degrees. b) Find the percentage and percent SE of people in the sample with college degrees. c) Estimate the chance that between 20% and 21% of the people in the sample will have college degrees. d) Find the correction factor and the corrected percent SE.
  1. (8 pts.) In a day’s production of widgets, a simple random sample of 250 widgets found that the average weight of a widget was 28 ounces with an SD of 0.4 ounces. a) Estimate the weight of a widget as a give-or-take number. b) Give a 95%-confidence interval for the weight of a widget.
  2. (15 pts.) A gambler asserts that a coin is biased, that it lands showing heads too often. He flips 400 times and it lands on heads 219 times. a) Briefly state the null and alternative hypothesis. b) Based on the null hypothesis, what is the expected value for 400 coin tosses? c) Estimate the SD and appropriate SE. d) Calculate the z - statistic for the experiment. e) Calculate the P - value for the experiment. What do you conclude?
  1. (7 pts.) For 100 random draws made from a box with replacement, the average of the draws was 33.5, and the SD was 20. Someone claims the average of the box is 30. What do you conclude?
  2. (12 pts.) Thirty-six draws are made from a box (Box A) that has an average of 80 and an SD of 18. Twenty-five draws are made from a second box (Box B) that has an average of 77 and an SD of 15. All draws are random draws with replacement. a) What is the appropriate SE for Box A? b) What is the appropriate SE for Box B? c) What is the combined SE for the two boxes? d) Estimate the difference of the averages of the two boxes as a give-or-take number.