Do You Really Know All About Confidence Intervals

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Do You Really Know All About Confidence Intervals?
If so, prove it !!!!!!

• Lecture 9B
• R. Mooring, Ph.D.
• Instructor

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Welcome to the Lecture 9B Game!!
Goal of the Game

• Be the first to answer the most questions right.
  If you do, you win.

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How To Play

• The game is played with four teams of five (or
  three) players each. The instructor will use a
  systematic sampling method to randomly assign
  each player to a team.
• The team can use calculators, their textbooks,
  pen, pencil, or paper to solve any problems but
  no computers.
• Teams can talk amongst themselves, but it would
  be detrimental to talk loud enough for other
  groups to overhear.

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How to Play

• The game show host (instructor) will ask easy,
  medium, hard, and extremely hard questions from
  chapters 18 and 19 of your textbook.
• The group that answers correctly first will
  receive all of the points for that question.
  (Groups that want to answer must have their
  representative raise their hand and be recognized
  by the host before answering.)
• In the event of a tie, the tie will be broken by
  an independent judge.
• If a group answers wrong, they must wait until
  all of the other groups have a chance to answer
  before answering again. If after a second round,
  no group gets the answer correct, the question
  will be discarded and play will continue with the
  next question.
• Each easy question is worth 5 points, the medium
  questions are worth 10 points, the hard questions
  are worth 20 points, and the extremely hard
  questions 25 points.

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How to Win

• The team with the highest number of points at the
  end of the game wins.
• In the event of a tie, both teams will be crowned
  co-winners and will receive the same award. If
  this is the case, there will not be a second
  place team.

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Why should you actively participate?

• The first place team will earn 40 class
  participation points.
• The second place team will earn 30 points.
• Third place will earn 25 points.
• Fourth place will earn 20 points.
• The game will take the place of two (2) class
  participation questions.

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Any questions?

• If not, then lets get started.

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EASY QUESTIONS

• 5 POINTS EACH

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Number 1

• The 95 confidence interval of a proportion is
• (0.15,0.45).
• How much was the value of the sample proportion?

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Number 2

• If the 99 confidence interval of a certain
  parameter is
• (123,672) ,
• How much is the margin of error?

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Number 3

• If the sample proportion of green MMs in a
  factory is 0.22 and the margin of error is /-
  .05 at 95 confidence, find the confidence
  interval of the proportion of green MMs.

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Number 4

• 2 Part Question (Must get both right for the
  points)
• 1) What level of significance is represented by Z
  1.645?
• 2) By Z 2.575?

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Number 5

• 29 of MATH 1231 students at Clayton State are
  non-traditional students. If we randomly pick 45
  MATH 1231 students, calculate the standard error
  of the number of non-traditional students.
• (Use 2 Decimal Places only!
• Do not put into a percent.)

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MEDIUM QUESTIONS

• 10 POINTS EACH

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Number 6

• What level of confidence is represented by Z
  2.12?

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Number 7

• What Z-value represents 79.6 confidence?

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Number 8

• The margin of error in my study is /- 4. If my
  standard error is 2.72, what is my critical
  value (Use 2 Decimals only!!)?

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Number 9

• Fill in the Blank with a word or phrase.
• For a given level of confidence, dividing the
  margin of error by three requires a sample
  ________ as large.

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Number 10

• How confident can I be of my parameter value if
  the margin of error derived by my sample
  statistic is /- 12 and the standard error is
  6.122? (Round to the nearest whole number.)

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HARD QUESTIONS

• 20 POINTS EACH

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Number 11

• Suppose the mean weight of a piece of candy is 6
  grams and the standard deviation is 1.2 grams.
  Whats the standard error of the mean weight of a
  handful of 22 pieces of candy?
• (Report 2 Decimal Places Remember the units)

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Number 12

• If I am willing to accept a margin of error of
  /- 4 of an estimate of a proportion (62) but
  want 99 confidence, how many items will I need
  to use? (Round up to the nearest whole number
  even if the decimal part is less than .5)

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Number 13

• A newspaper reports that the governors approval
  rating stands at 65. The article adds that the
  poll is based on a random sample of 972 adults
  and has a margin of /- 2.5 . What level of
  confidence did the pollsters use?
• (Round off critical value to 2 decimal places
• before continuing to answer the question.
• Use 2 Decimal Places only in the answer.)

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Number 14

• In 1998, a San Diego reproductive clinic
  reported 49 births to 207 women under the age of
  40 who had previously been unable to conceive.
  Find the 90 confidence interval for the success
  rate at this clinic.
• (Use only the first two decimal places of the
  sample proportion to solve the problem But make
  sure that you round properly.
• Use the first four decimal places of the
  standard error.
• Report 2 Decimal Places.)

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Number 15

• Direct mail advertisers send solicitations to
  thousands of potential customers in the hope that
  some will buy the companys product. The
  response rate is usually quite low. Suppose a
  company wants to test the response of a new
  flyer, and sends it to 1000 people randomly
  selected from their mailing list of over 200,000
  people. They get orders from 123 of the
  recipients. Create a 90 confidence interval for
  the percentage of people the company contacts who
  may buy something.
• (Use the first four decimals of the margin of
  error.
• Report only 2 decimals for the confidence
  interval.)

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EXTREMELY HARD QUESTIONS

• 25 POINTS

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Number 16

• National data in the 1960s showed that about
  44 of the adult population had never smoked
  cigarettes. In 1995, a national health survey
  interviewed a random sample of 881 adults and
  found that 52 had never been smokers. Create a
  95 confidence interval for the proportion of
  adults (in 1995) who had never been smokers.
• (Report 2 decimal places.
• Use 1.96 for the critical value, not 2.
• Keep 4 decimals for the standard error.)

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Number 17

• The average length of a fruit fly is 2 mm and
  has a standard deviation of 0.3 mm.
• The distribution of the lengths of the flies is
  unimodal and approximately symmetric.
• About what percent of the fruit flies should be
  2.5 mm or longer?
• (Use two decimals in the final answer.)

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Number 18

• Fruit flies eat an average of 6 pieces of fruit
  per year with a standard deviation of 0.8 fruit.
  If I pick a fruit fly at random, whats the
  approximate probability that the fruit fly eats
  7.6 fruit per year?

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Number 19

• If I sampled 4 fruit flies, what is the
  probability that my sample of flies eats on
  average, 5 fruit flies or less per year? (Use 2
  decimal places!!!)
• Let µ 6 fruit, s 0.8 fruit (Same as 8)

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Number 20

• You pay 10 and roll a die. If you get a 6, you
  win 50. If not, you get to roll again. If you
  get a 6 this time, you get your 10 back.
• Find the expected value of your prospective
  winnings.

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GAME OVER

• Thanks for playing the Lecture 9B game.
• Hope you enjoyed it.
• Remember, test 3 is Monday, October 23, 2006
  during class.

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Answers

• 1. 0.30
• 2. 274.5
• 3. (.17,.27)
• 4. 90 99
• 5. .07
• 6. 96.6
• 7. Z 1.27
• 8. Z 1.47
• 9. Nine times
• 10. 95

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Answers

• 11. 0.26 g
• 12. 977
• 13. 89.68
• 14. (.19,.29)
• 15. (.11,.13)
• 16. (.49,.55)
• 17. 4.75
• 18. 2.5
• 19. 0.62
• 20. -.28