Confidence Intervals for Means

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# Confidence Intervals for Means - PowerPoint PPT Presentation

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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### 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?
• 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).
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.
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