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Chi-Squared confidence intervals
- Intro Lesson22:37
- Lesson: 1a1:24
- Lesson: 1b0:45
- Lesson: 2a7:31
- Lesson: 2b11:21
- Lesson: 311:23
- Lesson: 413:25
Chi-Squared confidence intervals
Lessons
To estimate a population variance a Chi-Squared distribution is used,
• Chi-Squared: X2=σ2(n−1)s2
n: sample size
s: sample standard deviation
σ: population standard deviation
(n−1): is also called "degrees of freedom"
• Chi-Square table gives critical value area to the right
The Confidence interval for the variance is given by:
• XR2(n−1)s2 < σ2 < XL2(n−1)s2
• Chi-Squared: X2=σ2(n−1)s2
n: sample size
s: sample standard deviation
σ: population standard deviation
(n−1): is also called "degrees of freedom"
• Chi-Square table gives critical value area to the right
The Confidence interval for the variance is given by:
• XR2(n−1)s2 < σ2 < XL2(n−1)s2
- IntroductionWhat are Chi-Squared Confidence Intervals?
- 1.Determining Degrees of Freedom
How many degrees of freedom does a sample of size,a)7 have?b)20 have? - 2.Determining the Critical Value for a Chi-Square Distribution (XR2 and XL2)
If a Chi-Squared distribution has 8 degrees of freedom find XR2 and XL2, with aa)95% confidence levelb)99% confidence level - 3.Determining the Confidence Interval for Variance
Road and racing bicycles have an average wheel diameter of 622mm. From a sample of 15 bicycles it was found that the wheel diameters have a variance of 10mm. With a 90% confidence level give a range where the variance of all road and racing bicycle wheels lie. - 4.Determining the Confidence Interval for Standard Deviation
A Soda-pop company "Jim's Old Fashion Soda" is designing their bottling machine. After making 41 bottles they find that their bottles have an average of 335mL of liquid with a standard deviation of 3mL. With a 99% confidence level what is the range of standard deviation that this machine will output per bottle?