7.2 Fundamentals of Hypothesis Testing
Objectives: 1. To write the null hypothesis (H0) and the alternative hypothesis (H1).
2. To define critical regions and critical values.
3. To use the two-tailed test, right-tailed test, and left-tailed test to find critical values that allow us to
reject the H0.
Last chapter we used sample data to estimate population parameters.
This chapter we are testing those claims made about the population parameter.
We are trying to
determine if the sample results differ from the claim by an amount that is statistically significant.
Hypothesis – Claim or statement about a property of a population.
Ex: Examine the given statement, and then express the null hypothesis H0, and alternative hypothesis, H1.
1)
The mean age of smokers is greater than 19 years.
2)
The percentage of viewers tuned into the Super Bowl is equal to 71%.
3)
Salaries among computer scientists have a standard deviation less than $1500.
Critical Region –
Two-Tailed Test
Right-Tailed Test
Left-Tailed Test
Use When:
Use When:
Use When:
Find the critical z values. Sketch an example of the normal curve. In each case, assume that the normal distribution
applies.
1)
Two-tailed test; α = 0.25
2)
Right-tailed test; α = 0.05
3)
Left-tailed test; α = 0.28
4)
α = 0.08; H1 is µ ≠ 170
5)
α = 0.005; H1 is µ > 30
6)
α = 0.005; H1 is µ < 15
7)
α = 0.045; H0 is µ ≥ 15
8) α = 0.05; H0 is µ ≤ 15
9) α = 0.04; H0 is µ = 1.6