Upload
stephen-ochoa
View
25
Download
0
Embed Size (px)
DESCRIPTION
Inference on Proportions. Assumptions:. SRS Normal distribution np > 10 & n(1-p) > 10 Population is at least 10n. Normal curve. Formula for Confidence interval:. - PowerPoint PPT Presentation
Citation preview
SRSNormal distribution
np > 10 & n(1-p) > 10
Population is at least 10n
statistic of SD valuecritical statisticCI
p̂
npp 1*z
Normal curve
Note: For confidence intervals, we DO NOT know p – so we MUST substitute p-hat for pin both the SD & when checking assumptions.
A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.
Assumptions:
•Have an SRS of adults
•np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both are greater than 10, the distribution can be approximated by a normal curve
•Population of adults is at least 10,120.
41,.35.1012
)62(.38.96.138.
1*ˆ
npp
zP
Using methods such as these, the interval between 35% and 41% captures the true proportion of adults who believe in ghosts 95% of the time.
Step 1: check assumptions!
Step 2: make calculations
Step 3: conclusion in context
Another Gallop Poll is taken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval?
To find sample size:
However, since we have not yet taken a sample, we do not know a p-hat (or p) to use!
npp
zm1
*
.1(.9) = .09
.2(.8) = .16
.3(.7) = .21
.4(.6) = .24
.5(.5) = .25
By using .5 for p-hat, we are using the worst-case scenario and using the largest SD in our calculations.
Another Gallop Poll is taken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval?
60125.600
25.96.104.
5.5.96.104.
5.5.96.104.
1*
2
n
n
n
n
npp
zm
Use p-hat = .5
Divide by 1.96
Square both sides
Round up on sample size
H0: p = valueHa: p > valuewhere p is the true proportion of context
Use >, <, or ≠
statistic of SD
parameter - statisticstatisticTest
z npp
pp
1
ˆ
A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product. The radio station conducts a random sample of 400 people and finds that 90 have heard the ad and recognize the product. Is this sufficient evidence for the company to renew its contract?
Assumptions:
•Have an SRS of people
•np = 400(.2) = 80 & n(1-p) = 400(.8) = 320 - Since both are greater than 10, this distribution is approximately normal.
•Population of people is at least 4000.
H0: p = .2 where p is the true proportion of people who
Ha: p > .2 heard the ad
05.α1056.25.1
400)8(.2.
2.225.
valuepz
Since the p-value >, I fail to reject the null hypothesis. There is not sufficient evidence to suggest that the true proportion of people who heard the ad is greater than .2.
Use the parameter in the null hypothesis to check assumptions!
Use the parameter in the null hypothesis to calculate standard
deviation!