- Home
- AS-Level Maths
- Hypothesis Testing
Confidence levels, significance levels and critical values
- Intro Lesson23:12
- Lesson: 1a4:38
- Lesson: 1b3:13
- Lesson: 1c5:51
- Lesson: 2a3:42
- Lesson: 2b3:04
- Lesson: 2c3:42
- Lesson: 35:19
- Lesson: 45:58
- Lesson: 510:18
Confidence levels, significance levels and critical values
Basic Concepts: Measures of relative standing - z-score, quartiles, percentiles, Introduction to normal distribution
Lessons
- IntroductionUsing sample data, it is possible to find a Z-score relating to the claim (the test-statistic).
Significance level
Confidence Level (1−α)
Significance Level (α)
Critical Value (Zα)
0.90
0.10
?
0.95
0.05
?
0.99
0.01
?
Left Tail Test:
.
Right Tail Test:
.
Two tailed Test:
.
- 1.Finding the Critical Value
With a significance level of α=0.075 what is the resulting critical value of:a)A right-tailed test?b)A left-tailed test?c)A two-tailed test? - 2.Find the critical value from the following confidence levels for a right-tailed test:a)90% confidenceb)95% confidencec)99% confidence
- 3.Rejecting or Failing to Reject the Null Hypothesis
The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:
H0: p≤0.5
H1: p > 0.5
Using a significance level of 0.10 (which corresponds to a critical value of Zα=1.28), and a Z-score of Z=1.40 relating to our Null Hypothesis;
Can we reject the Null Hypothesis? - 4.The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:
H0: μ≥175lbs
H1: μ < 175lbs
Using a 95% confidence level and a Z-score of Z=-1.50 relating to our Null Hypothesis;
Can we reject the Null Hypothesis? - 5.The following claim is made.
"70% of Canadians own a pet".
Given that the test-statistic is Z=2.75, with a confidence level of 90% what can be said about the proportions of pet owners in Canada?