Sample Size Determination

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# Sample Size Determination - PowerPoint PPT Presentation

Sample Size Determination. Everything You Ever Wanted to Know About Sampling Distributions--And More!. Sampling Distribution. A frequency distribution of all the means obtained from all the samples of a given size Example: \$\$ spent on CD’s at Best Buy Daffy \$34.00 Donald \$72.00

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## PowerPoint Slideshow about 'Sample Size Determination' - hailey

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### Sample Size Determination

Everything You Ever Wanted to Know About Sampling Distributions--And More!

Sampling Distribution
• A frequency distribution of all the means obtained from all the samples of a given size
• Example: \$\$ spent on CD’s at Best Buy
• Daffy \$34.00
• Donald \$72.00
• Sylvester \$36.00
• Tweetie Bird \$40.00
• All samples of n=2
• Develop a sampling distribution using n=2
• Calculate the population mean

CAR

A B C D E

Expected 3 4 5 0 1

Life

Sampling Distributions
• The distribution of sample means is skinnier than the distribution of elements
• Why?
• The distribution is normal
• The sampling distribution mean equals the population mean
Standard Error
• The variability in the sampling distribution
• Tells you how reliable your estimate of the population mean is
• If this is big (good or bad)
• If this is small (good or bad)
• WHY?
Standard Error

Sxstandard deviation

square root of the sample size

As the samples size gets bigger, the standard error gets __________

Confidence Intervals
• CI= Xbar +/- z (standard error)
• Where:
• z= _____ for 68% confidence
• z= _____ for 95% confidence
• z= _____ for 99.7% confidence
• (again think Chebychev)
• What confidence level should you use?
Develop a Confidence Interval
• Estimate the average number of trips to the beach taken by undergrad students during their 4-6 year career
• xbar = 5
• SD = 1.5
• 95% Confidence Level
• n=100
So,
• There is a 95% chance that if all undergrad students were sampled regarding the number of beach trips that the findings would differ from our results by no more than ____ in either direction.
or, maybe better,
• If I were to conduct this study 100 times, then I would get _____ different confidence intervals. If I have a 95% confidence interval then ____ of the 100 CI’s will contain the true population mean (mu) and ____ will not.
• I sure hope that the confidence interval I got is one of the 95 that contains mu!
Probably the easiest interpretation:
• If you have a 95% Confidence Interval - there is a 95% chance that the CI will contain Mu – there is a 5% chance that it won’t.
Confidence Interval Issues
• Reliability (Z)
• how often we are correct – how often mu falls within the range
• Precision
• how wide the confidence interval is
• The smaller the n, the _____ the CI
• Given a particular n, the CI will be _______ when we increase the reliability
Factors that Influence n
• Precision (H)
• how skinny must your CI be in order to be able to take action on the results?
• I will go to a new water park in the area.
• DWN PWN Maybe PW DW
• I will pay _____ for a musical card.
• I will pay _____ for a motorcycle.
More Factors That Influence n
• Confidence level (z)
• Population SD
• Time, money and personnel
Sample Size for Interval or Ratio Data

Z2

n= H2 * s2

Where:

z= 1, 1.96, or 3

H= precision (+/-) H

s2= variance (or standard deviation squared)

Sample Size for Nominal or Ordinal Data

Z2

n = H2 * (P) (Q)

Where:

Z= 1, 1.96, or 3

H= a percentage (e.g., 0.03--NOT 3)

P = initial estimate of the population proportion

Q= (1-P)

n for Proportion of Students Who Read the News Paper
• Do you read the newsl paper?
• 1. YES
• 2. NO
• Estimate that 60% read the news paper
• Want a 99 % CI
• Want a +/- 3% precision
The Final Sample Size
• Compute n for all nominal, interval and ratio questions
• most conservative
• limited resources
Non-statistical Approaches to Sample Size (n)
• All you can afford method:
• subtract costs from budget
• figure out cost per interview
• divide leftover budget by cost per interview
• Rules of thumb