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Exam 3 Practice Questions - Basic Statistics | MATH 160, Exams of Statistics

University of Arizona (UA)Statistics

Material Type: Exam; Class: Basic Statistics; Subject: Mathematics Main; University: University of Arizona; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

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Practice Test for Statistics (Math 160), Exam 3
1) A class survey in a large class for 1st year college students asked, “about how many
minutes do you study on a typical weekend?” The mean response of the 269 students
was 137 minutes. Suppose that we know that the study time follows a Normal
distribution with standard deviation of 65 minutes in the population of all first-year
students at this university.
a) Use the survey to give a 99% confidence interval for the mean study time of all
the first-year students.
b) What condition not yet mentioned is needed for your confidence interval to be
valid?
c) For this problem, give an example how the condition in part (b) might not be
satisfied.
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Practice Test for Statistics (Math 160), Exam 3

  1. A class survey in a large class for 1st^ year college students asked, “about how many minutes do you study on a typical weekend?” The mean response of the 269 students was 137 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation of 65 minutes in the population of all first-year students at this university. a) Use the survey to give a 99% confidence interval for the mean study time of all the first-year students. b) What condition not yet mentioned is needed for your confidence interval to be valid? c) For this problem, give an example how the condition in part (b) might not be satisfied.
  1. To assess the accuracy of a laboratory scale, a standard weight known to 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (if there were no random deviation, this mean would be 10 grams). The standard deviation of the scale readings is known to be .0002 grams. a) Standard deviation is supposed to measure “spread.” Qualitatively describe the spread of the weight's distribution. b) The weight is weighed five times. The mean result is 10.0023 grams. Give a 98% confidence interval for the mean of repeated measurements of the weight. c) How many measurements must be averaged to get a margin of error of plus or minus .0001 with 98% confidence? d) Now suppose the true standard deviation is unknown, but we compute s =. grams (the computed mean is still 10.0023 grams). Find a 98% confidence interval. e) Your interval for part (d) should be larger than in part (b). Why?
  1. A government report says that a 90% confidence interval for the mean income of American households is $59,067 with a margin of error of $356. Is the mean income significantly different from $59,000? (Multiple choice, explain your answer) a) It is not significantly different as the 10% level and therefore is also not significantly different at the 5% level. b) It is significantly different at the 10% level but might be significantly different at the 5% level. c) It is significantly different at the 10% level. True or False (explain your answer)
  2. T F z -tests are strongly influenced by outliers.
  3. T F If we would like to increase the power of a test, we should decrease the sample size.
  4. T F If we increase α from .05 to .10, the power of a test will increase. (Hint: What is α?)
  5. T F If the hypothesized mean is increased, the power of the test is decreased.
  6. T F If we would like to increase the effect size which is practically significant, we should decrease the sample size.
  1. Here are measurements in millimeters of a critical dimension for 16 auto engine crankshafts. 224.120 224.001 224.017 223.982 223.989 223. 223.960 224.089 223.987 223.976 223.902 223. 224.098 224.057 223.913 223. The dimension is supposed to be 224 mm and the variability of the manufacturing process is unknown. Is there evidence that the mean dimension is not 224mm?
  2. The Trial Urban District Assessment (TUDA) is a government sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a basic reading level and a score of 281 is proficient. Scores for a random sample of 1470 eighth graders in Atlanta had a mean score of 240 with standard error of 1.1. a) Give a 99% confidence interval for the mean score of all Atlanta eighth graders. b) Is there good evidence that the mean for all Atlanta eighth graders is less than the basic level?