Sample Sizes And Confidence Interval For Mean And Proportion BP 1

Sample sizes and confidence intervals for proportions
Chong Chun Wie
Ext: 2768
[e-mail]

Content
• Sampling distribution of sample means (SDSM)
• Normality Test
• Estimating a population mean: σ known
• Estimating a population mean: σ unknown
• Standard deviation of proportion
• Confidence interval of proportion
• Hypothesis testing with proportion

Population and Sample

Samples

Populations

Sampling distribution of sample means (SDSM)

Sampling distribution
• Example
– Select randomly from the following number (1, 1, 2, 5, 5,
6, 7, 10)
– Mean = 4.625
•
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If we choose 3 points randomly and produced the mean
1, 1, 2 = 4, mean = 1.33
2, 5, 6 = 13, mean = 4.33
1, 5, 7 = 13, mean = 4.33
2, 6, 7 = 15, mean = 5
5, 1, 10 = 16, mean = 5.33

Sampling distributions for (a) normal, (b) reverse-Jshaped, and (c) uniform variables

Test for normality
• Shapiro-Wilk Test (SPSS)
• Probability Plot (Minitab)

Estimating a population mean: σ known

Confidence Interval for µ using normal distribution

95% confidence interval
• Suppose we want to construct a 95% confidence interval for μ,

Another word: 95% of all sample means are in the interval

Margin of Error

Z table

95% confidence α = 0.05
99%
confidence α = 0.01

Example 1
• A doctor graduated from IMU is setting up a new clinic in KL. Before operation, he wants to know the average charge for common illness (e.g. flu). He asked his friends and relatives to record the consultation fees they paid during their last visit to clinic, and managed to get 30 separate records with a mean of RM62. It is known that the standard deviation of all the records is RM8 and the data is normally distributed.
• Construct a 95% confidence interval for the mean charge of common illness in KL’s clinics.

Solution 1

Note
• If the doctor had collected 100 records instead of 30, the 95% confidence interval will become RM61.20 and
RM62.80.
• The more sample we have, the narrower the confidence interval (the
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