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Math 116 - Chapters 14, 17, 18
Hypothesis testing and confidence intervals for one and two population means
Chapter 14 – ONE population mean - z procedures (sigma known)
Chapter 17 – ONE population mean - t procedures (sigma is unknown)
Assumptions
 We have a simple random sample
 The population is normally distributed or the sample size, n, is large (n > 30). For very skewed distributions
use the procedures when n is 40 or more
The procedure is robust, which means that minor departures from normality will not adversely affect the results of
the test. However, for small samples, if the data are very skewed and have outliers, the procedure should not be
used.
Use dot plots and stem and leaf plots to check whether the t-procedures can be used.
A normal probability plot plots observed data versus normal scores. If the normal probability plot is roughly linear and all
the data lie within the bounds provided by the software (our calculator does not show the bounds), then we have reason to
believe the data come from a population that is approximately normal.
CALCULATOR
z- Test, T-Test, Z-Interval, T-Interval
Chapter 17 – Matched pairs – t procedures
A sampling method is dependent when the individuals selected to be in one sample are used to determine the
individuals to be in the second sample.
Assumptions:
1. The sample is obtained using simple random sampling
2. The sample data are matched pairs
3. The differences are normally distributed with no outliers or the sample size, n, is large (n ≥ 40)
Procedure
Take the difference d of the data pairs. Find the mean difference d-bar. Perform a t-test on d-bar with n-1 degrees
of freedom.
CALCULATOR:
T-Test or T-Interval
Chapter 18 - Hypothesis testing and confidence intervals for two populations – Independent
samples - Population Standard Deviations not Assumed Equal (Non-Pooled t-Test)
Assumptions
 The samples are obtained using simple random sampling
 The samples are independent
 The populations from which the samples are drawn are normally distributed or the sample sizes are large
( n1
 40, n2  40 )
The procedure is robust, so minor departures from normality will not adversely affect the results. If the data have
outliers, the procedure should not be used.
CALCULATOR:
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2-Samp-T –Test or 2-Samp-T-Interval (NON – Pooled)
For all the problems make sure you do the following:
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What is the variable? Include units
Identify the problem as (1) 1 sample, (2) two dependent samples: matched pairs, (3) two
independent samples
To determine whether t-procedures can be used
o Sketch a stem and leaf plot or a dot plot to explore the shape
o Sketch a normal probability plot and a box plot to explore the shape and List relevant
parameters/statistics and label with correct symbols (if some of the statistics are not
given, use the calculator to find them)
To answer the questions about HYPOTHESIS TESTING:
o Write hypotheses
o Sketch graph, shade and label – include possible locations of x-bar
o Use the calculator to test the hypothesis, and write results
o Explain the meaning of p-value in symbols and in words
o Write conclusion within context
To answer questions about CONFIDENCE INTERVALS
o Use calculator to obtain results
o Does the interval agree with the hypothesis testing conclusion? Explain why
Just for fun section: using formulas and procedures to find:
o The test-statistic t
o The p-value
o The confidence interval
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