{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lect17v1_2up_1up - Stat 104 Quantitative Methods for...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 104: Quantitative Methods for Economists Class 17: Confidence Intervals- One Sample Proportion 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
What is a sample proportion? square6 Say we survey n people and ask them if they like the movie The Social Network (yes or no). We obtain n responses of the form X i = 1 if y es square6 The true (but unknown) population proportion of people who like the movie is p so that P(X i =1)= p . square6 We can estimate p by using 2 0 if n o $ p X n X i i n = = = 1 1
Background image of page 2
1 1 1 0 3 0 1 $ p = 4 6
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Another Student Survey Sample Member Student ID Do you smoke regularly? Numerical Coding 1 232923 No 0 2 234932 Yes 1 3 Yes 1 4 No 0 : : : : 49 No 0 50 Yes 1 11 ˆ 22%. 50 p = = Suppose that 11 of the 50 students surveyed report that they regularly smoke. The sample proportion is 4
Background image of page 4
The Central Limit Theorem Works for Proportions square6 If a random sample of size n is obtained from some population where the probability of having some characteristic is p , then (for large sample sizes) 5 (1 ) ˆ ~ , p p p N p n -
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example square6 If the true proportion of voters who support Proposition A is p = .4, what is the probability that a sample of size 200 yields a sample proportion between .40 and .45? square6 i.e.: if p = .4 and n = 200, what is P(.40 p .45) ? ^ 6
Background image of page 6
Example square6 if p = .4 and n = 200, what is P(.40 p .45) ? ˆ p(1 p) .4(1 .4) σ .03464 n 200 p - - = = = Find : ˆ p σ ^ .40 .40 .45 .40 ˆ P(.40 .45) P z .03464 .03464 P(0 z 1.44) p - - = = Convert to standard normal: Use standard normal table: P(0 z 1.44) = .4251 7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Confidence Intervals for Proportions square6 Using the same logic as before for means, a (1- α) 100% confidence interval is given by $ ( $ ) p p ± - 1 square6 We always assume n is big (larger than 30) when estimating proportions . 8 $ / p z n α 2
Background image of page 8
The critical value square6 The 95% confidence interval is usually used, but some other favorites are 90% and 99% 9
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example: A marketing research firm contacts a random sample of 100 men in Chicago and finds that 40% of them prefer the Gillette Sensor razor to all other brands. The 95% C.I. for the proportion of all men in Chicago who prefer the Gillette Sensor is determined as follows: 0.40(1 0.40) 0.40 1.96 0.40 1.96(0.05) (0.30398,0.49602) - ± = ± = 10 100 So with 95% confidence, we estimate the proportion of all men in Chicago who prefer the Gillette Sensor to be somewhere between 30 and 50 percent (pretty good market share).
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}