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Interval Estimation For Means (Margin of Error)

 

Interval estimation involves using sample data to determine a range (interval) that, at an established level of confidence, that is expected to contain the mean of the population.

Steps

1.   Determine confidence level (df=n-1; alpha .05, 2-tailed)

2.   Use either z distribution (if n>120) or t distribution (for all sizes of n).

3.   Use the appropriate table to find the critical value for a 2-tailed test

4.   Multiple hypotheses can be compared with the estimated interval for the population to determine their significance. In other words, differing values of population means can be compared with the interval estimation to determine if the hypothesized population means fall within the region of rejection.

 

Estimation Formula

where

= sample mean

CV = critical value (consult distribution table for df=n-1 and chosen alpha-- commonly .05)

 = Standard error of the mean

 

Note: assumes sample standard deviation was calculated using:

 

Example: Interval Estimation for Means

 

Problem: A random sample of 30 incoming college freshmen revealed the following statistics: mean age 19.5 years; sample standard deviation 1.2. Based on a 5% chance of error, estimate the range of possible mean ages for all incoming college freshmen.

Estimation

Critical value (CV)

Df=n-1 or 29

Consult t-distribution for alpha .05, 2-tailed

CV=2.045

Standard error

Estimate

Interpretation

We are 95% confident that the actual mean age of the all incoming freshmen will be somewhere between 19 years (the lower limit) and 20 years (the upper limit) of age.

 

Software Output Example


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