Page 592 - Probability and Statistical Inference

13

Sample Size Determination:

Two-Stage Procedures

13.1 Introduction

2
Consider a sequence of iid observations X , X , ... from a N(µ, σ ) population
1
2
where both parameters µ ∈ ℜ, σ ∈ ℜ are unknown. Having recorded a fixed
+
number of observations X , ..., X , n ≥ 2, and with preassigned σ ∈ (0, 1), the
1
n
customary 100(1 − α)% confidence interval for the population mean µ is
given by

Here, and t stands for
n−1,α/2
the upper 100(α/2)% point of the Student’s t distribution with (n − 1) degrees
of freedom.

Figure 13.1.1. The Area on the Right (or Left) of t n−1,α/2
(or −t ) Is α/2
n−1,α/2
The width of the confidence interval J is given by
n

Note that the width W is a random variable even though n is
n
held fixed. It is so because S is a random variable.
n
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