BUSS1020 Chapter Notes - Chapter 8: Confidence Interval, Standard Deviation, Point Estimation
28 May 2018
School
Department
Course
Professor
CHAPTER 8: CONFIDENCE INTERVALS
• Confidence interval: used to determine the percentage of sample means within certain distances of pop mean
o Confidence level (1-α): confidence that interval will contain the unknown pop parameter
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CONFIDENCE INTERVAL ESTIMATE FOR THE MEAN (σ KNOWN)
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= point estimate
o Zα/2 = critical value
• Assumptions:
o Population standard deviation is known
o Population is normally distributed OR use large sample (CLT)
• Finding critical value Zα/2
o 95% confidence interval à Confidence level = 1 – α = 0.05
o In table find 0.975 (0.05) à Zα/2 value = 1.96
CONFIDENCE INTERVALL ESTIMATE FOR THE MEAN (σ UNKNOWN)
• In the majority of real world business situations, σ is not exactly known à use sample SD instead = S
o Introduces more uncertainty
•
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• Student-t distribution:
o σ unknown
o Population is normally distributed OR use large sample if not (CLT)
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o As n increases, t distribution approaches standardized normal distribution (n>= 120 = virtually identical)
CONFIDENCE INTERVALL ESTIMATE FOR THE PROPORTION
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• Distribution of proportion is approx. normal if
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- p = sample proportion
- n = sample size
- π = population proportion
