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Used
to compare a mean from a random sample to the mean (mu) of a population. It is especially useful to compare a mean from a
random sample to an established data source such as census data to ensure you have an
unbiased sample. Examples include comparing
mean age and education levels of survey respondents to known values in the population.
Problem:
Compare the mean age of incoming students to the known mean age for all previous incoming
students. A random sample of 30 incoming college freshmen revealed the following
statistics: mean age 19.5 years, standard deviation 1 year. The college database shows the
mean age for previous incoming students was 18.
Assumptions
Interval/ratio
level data
Random
sampling
Normal
distribution in population
State
the Hypothesis
Ho:
There is no significant difference between the mean age of past college students and the
mean age of current incoming college students.
Ha:
There is a significant difference between the mean age of past college students and the
mean age of current incoming college students.
Set
the Rejection Criteria
Significance
level .05 alpha,
2-tailed test
Degrees
of Freedom = n-1 or 29
Critical
value
from t-distribution
= 2.045
Compute
the Test Statistic
Standard
error
of the sample mean
Test
statistic
 
Decide
Results of Null Hypothesis
Given
that the test statistic (8.197) exceeds the critical value (2.045), the null hypothesis is
rejected in favor of the alternative. There is a statistically significant difference
between the mean age of the current class of incoming students and the mean age of
freshman students from past years. In other words, this year's freshman class is on
average older than freshmen from prior years.
If
the results had not been significant, the null hypothesis would not have been rejected.
This would be interpreted as the following: There is insufficient evidence to conclude
there is a statistically significant difference in the ages of current and past freshman
students.
Software Output Example
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