University:
Montgomery College
Course:
MATH 117: Elements of Statistics
Academic year:

2020
Views:

195

Pages:

2
Author:

Alma Hester

Chapter 8 – Confidence Interval – One Population Section 8.1 - Estimating a Population Mean: σ Known Assumptions: • • • The sample is a simple random sample The value of the population standard deviation σ is known. Either or both of these conditions are satisfied: i) The population is normally distributed, or ii) n ≥ 30 (The sample has 30 or more values) Procedure for Constructing a Confidence Interval for μ (with Known σ) 1. Verify that the required assumptions are satisfied. 2. Find the critical value z c (from table 5). 3. Evaluate the margin of error E. (E = zc  ) n 4. Then using E and the sample mean the confidence interval is: x−E  x+E or ( x − E, x + E ) Using the TI-83 to Construct Confidence Intervals for μ: STAT>>TESTS select 7:ZInterval Round-off Rule for Confidence Intervals used to Estimate μ: a) If original data is given: use one more decimal place than original values. b) If you are given summary statistics from a data set, use the same number of decimal places used for the sample mean. SAMPLE SIZE FORMULAS (Look at the book and copy them here) Do one of the problems from the book about sample size. QUESTION I - At the same confidence level, does a larger sample size produce a shorter (more precise) interval or a larger (less precise interval)? By computing 1-a and 1-b, you will be able to answer this question. QUESTION 2 – If we keep the same sample size and increase the confidence level, what happens to the length of the interval? Comparing results from 1-a and 1-c will help you answer this question. 1) A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2. a) Compute the 90% confidence interval about µ if the sample size, n, is 45. b) Compute the 90% confidence interval about µ if the sample size, n, is 55. How does increasing the sample size affect the margin of error E? How does it affect the length of the interval? c) Compute the 98% confidence interval about µ if the sample size, n, is 45. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? How does it affect the length of the interval? d) Can we compute a confidence interval about µ based on the information given if the sample size is n = 15? Why? If the sample size is 15, what must be true regarding the population from which the sample was drawn? IMPORTANT: Before constructing a confidence interval by using this method described in our book, it is very important to check the requirements