Stat 100, Mar. 13

1
Stat 100, Mar. 13

• Read Chapter 18, Try problems 1-6, 10-11

2
A preliminary-

• During this lecture well use this result from
  earlier in the term
• For normal curve (bell-shaped)
• About 68 is in interval mean?? SD
• About 95 is in interval mean ? 2 SD
• About 99.7 is in interval mean ? 3 SD

3
Imagine coin flipping activity

• Everybody in the class flips a coin 64 times
• Each person finds proportion of his/her flips
  that are Heads
• We draw a histogram of the results.

4
Coin flip example continued

• Are some possibilities for the proportion (heads)
  more likely than others?
• What would be the shape of the histogram of the
  proportions from the different class members?

5
Rule For Sample Proportions

• Normal curve approximately describes possible
  sample proportions that could result from the
  many different possible samples in a random
  circumstance.

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Characteristics of this normal curve

• Mean population or theoretical value of the
  proportion (p)
• Std Dev

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Consider n64 coin flips

• Let pproportion that are heads
• True p 0.5
• Mean of curve for possible sample proportions is
  0.5
• St Dev is sqrt (0.5 x 0.5/64) 0.06

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From 68-95-99.7 Rule

• About 68 chance that sample proportion will be
  in range 0.50.06, or 44 to 56
• About 95 chance that sample proportion will be
  in range 0.50.12, or 38 to 62
• About 99.7 chance that sample proportion will be
  in range 0.50.18, or 32 to 68

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Application

• Suppose n64 people each tasted Pepsi and Coke in
  a blind experiment.
• The result is that 40/640.625, or 62.5 state a
  preference say the Coke tasted better.

10
Pepsi/Coke example

• Suppose everybody really picks preferred drink
  randomly
• So, picking preferred drink is like a coin flip.
  For instance, picking Coke might be like flipping
  Heads
• Results from n 64 people would be like results
  of 64 coin flips

11
Pepsi/Coke continued

• For 64 coin flips, we found that about 95 of the
  time the proportion heads will be in interval
  38 to 62
• Proportion will be greater than 62 only about
  2.5 of the time
• So, 62.5 picking Coke would be unusual if
  preferences are random (like coin flips)
• Inference Data might be evidence that
  preferences arent random

12
A past class activity

• Students picked a number between 1 and 10.
• N123 participated
• 29 students picked the number 7.
• Sample proportion is 29/123 .24 (24)

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For true random picks

• Proportion picking 7 would be p1/10 .1
• Mean sample p .1
• Std. Dev sqrt (.1 x.9 / 123) 0.027

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Do Students Pick Randomly?

• With random picks, chance is 99.7 that
  proportion picking 7 will be in interval
  .1 (3?.027), or .019 to .181
• The class result .24 picking 7 is well
  outside this interval.
• Inference Students probably dont pick randomly
  - observed result very unlikely to result from
  random selection