1. Estimating population mean µwith the assumption that σis
known (Normal distribution):
•Confidence interval:
¯x±z∗σ
√n
Table Cgives z∗for a given C% confidence level.
•Significance tests for the null hypothesis H0:µ=µ0:
The one sample ztest statistic:
z=¯x−µ0
σ/√n
Find the P-value of zusing Table A, do some algebra depending on
your alternative hypothesis Ha.
2. Estimating population mean µwith the assumption that σis not
known (t distribution):
•The one sample tconfidence interval:
¯x±t∗s
√n
Table Cgives t∗for a given C% confidence level and df =n−1.
•One sample significance tests for the null hypothesis H0:
µ=µ0:
The one sample tstatistic
t=¯x−µ0
s/√n,with df =n−1
Find the P-value of tusing Table C with df =n−1, take in con-
sideration whether you have a one sided or two sided alternative
hypothesis.
•Matched pairs: Use the above one sample procedures to analyze
matched pairs by taking the difference within each mathced pair to
produce a single sample.
3. Comparing two population means µ1and µ2with the assumption
that σ1and σ2are not known (t distribution):
•The two sample tconfidence interval:
¯x1−¯x2±t∗ss2
1
n1
+s2
2
n2
Table Cgives t∗for a given C% confidence level and df = min(n1−
1, n2−1).
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