Lec5.3a - 127 Lecture 13 CHAPTER 5 CONFIDENCE INTERVALS Small-Sample Confidence Intervals for a Population Mean Contd(Section 5.3 page 321 Recall

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
127 Lecture 13: CHAPTER 5: CONFIDENCE INTERVALS Small-Sample Confidence Intervals for a Population Mean – Cont’d (Section 5.3, page 321) Recall: Last class we introduced the student’s t-distribution which is used when the population is approximately normal and the sample size is small. n s x t follows the t-distribution with n-1 degrees of freedom. Confidence Intervals Using the Student’s t Distribution If a random sample X 1 , X 2 . . . X n is chosen from a normal distribution; then the confidence Interval of is SE t x df ) , 2 ( Example: The article “Direct Strut-and-Tie Model for Pre-stressed Deep Beams” presents measurements of the nominal shear strength (in kN) for a sample of 15 pre-stressed concrete beams. The results are 580 400 428 825 850 875 920 550 575 750 636 360 590 735 950 Assume the data come from a normal distribution and there are no outliers. Construct a 99% confidence interval for the mean shear strength. (Note: If it was not stated that the data follow a normal distribution, we would need to find out if it follows a normal distribution by either a histogram/boxplot because the sample is small. When the sample is small, we can not assume normality. We
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
128 need to be certain that there are no outliers and the distribution is symmetric.)
Background image of page 2
129 Example: For the data in the above example, if we wanted to find a 95% confidence interval instead of a 99% confidence interval, what value in the formula would change? What would the new CI become? Question: Considering these 2 examples, if the level of the confidence is decreased and all other things remain the same, the width of the confidence interval will ________________. Confidence Intervals for the Difference Between Two Means (Section 5.4, page 354) We now investigate examples in which we wish to estimate the difference between the means of two populations. The data will consist of two samples, one from each population. For this section, we will only be dealing with large sample means. Summary Let x n X X ,..., 1 be a large random sample of size x n from a population with mean x and standard deviation x , and let y n Y Y ,..., 1 be a large random sample of size y n from a population with mean y and standard deviation y . If the two samples are independent, then a level )% 1 ( 100 confidence interval for y x is y y x x n n z Y X 2 2 2 ) ( When the values of x and y are unknown, they can be replaced with the sample standard deviations x s and y s .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
130 Example: The chemical composition of soil varies with depth. Fifty
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/20/2011 for the course STAT 2800 taught by Professor Paula during the Winter '11 term at UOIT.

Page1 / 12

Lec5.3a - 127 Lecture 13 CHAPTER 5 CONFIDENCE INTERVALS Small-Sample Confidence Intervals for a Population Mean Contd(Section 5.3 page 321 Recall

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online