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Confidence Intervals for Means. point estimate – using a single value (or point) to approximate a population parameter. the sample mean is the best point estimate of the population mean  The problem is, with just one point, how do we know how good that estimate is?

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slide2
point estimate – using a single value (or point) to approximate a population parameter.
    • the sample mean is the best point estimate of the population mean 
  • The problem is, with just one point, how do we know how good that estimate is?
  • A confidence interval (or interval estimate) is a range of interval of values that is likely to contain the true value of the population parameter.
  • confidence interval = estimate  margin of error
  • common choices are:
    • 90% ( = 0.10);
    • 95% ( = 0.05);
    • 99% ( = 0.01).
slide3
When sample sizes are small, we must use the t-distribution instead of the normal curve (z-distribution). (Appendix C – p477)
  • This table relies on ‘degrees of freedom’, which is always n – 1.
slide4
Create a 95% confidence interval for the starting salaries of 20 college graduates who have taken a statistics course if the mean salary is $43,704, and the standard deviation is $9879.
  • margin of error

s = standard deviation = $9879

n = sample size = 20

df= degrees of freedom = n-1=19

tcrit=2.093

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