For a random sample of size
n taken from a random variable
X∼N(μ,σ2), the sample mean (
Xˉ) is normally distributed with
Xˉ∼N(μ,nσ2).
To perform the test:
- Define the test statistic
- Determine whether a one-tailed or two-tailed test is needed
- Identify the null and alternate hypotheses accordingly
- Calculate
P(Xˉ<xˉ) and/or
P(Xˉ>xˉ)
- Compare with the significance level of the test (usually
5%) and decide whether or not to reject the null hypothesis
- Conclude with a statement in context of the question
Sample mean of a Normally distributed random variable
Xˉ∼N(μ,nσ2)
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