STATISTICS AND PROBABILITY

Quarter 3-Week 10

Module 4: T-DISTRIBUTION AND CONFIDENCE INTERVAL

LESSON 1: CONFIDENCE INTERVAL

What's New:

When you make an estimate in statistics, whether it is a summary statistic or a test statistic, there is always uncertainty around that estimate because the number is based on a sample of the population you are studying. The confidence interval is the range of values that you expect your estimate to fall between a certain percentage.

Activity 1: FACT OR BLUFF Directions: Write FACT if the statement is correct otherwise write BLUFF.

________________1. The confidence level is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value.

________________2. A confidence interval is the standard deviation of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence.

________________3. Confidence, in statistics, is another way to describe probability.

________________4. You can calculate confidence intervals for many kinds of statistical estimates, including proportions and population means.

________________5. In the confidence interval there is an exact value that you expect your estimate to fall.

Governm NOT FOR STATISTICS AND PROBABILITY Quarter 3-Week 10 Module 4: T-DISTRIBUTION AND CONFIDENCE INTERVAL LESSON CONFIDENCE INTERVAL What's New When you make an estimate in statistics, whether it is a summary statistic or a test statistic, there is always uncertainty around that estimate because the number is based on a sample of the population you are studying. The confidence interval is the range of values that you expect your estimate to fall between a certain percentage. Activity 1: FACT OR BLUFF Directions: Write FACT if the statement is correct otherwise write BLUFF. 1. The confidence level is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value. 2. A confidence interval is the standard deviation of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. 3. Confidence, in statistics, is another way to describe probability 4. You can calculate confidence intervals for many kinds of statistical estimates, including proportions and population means. 5. In the confidence interval there is an exact value that you expect your estimate to fallSolution: Given: a = 0.01, Za =1.645, a =9000, E = 500 Substituting these values into the sample size formula: (1.645 .9000 )2 " - )=500 - 876.75 * 877 Therefore, he needs at least 877 families as sample. What's More Activity 1: Solve Me! Directions: Analyze and Solve the following problems completely. Write your solution in a coupon bond. 1. The mean and standard deviation for the quality grade - point averages of a random sample of 36 college seniors are calculated to be 2.6 and 0.3 respectively. Find the a. 95% confidence interval for the mean of the entire senior class b. 99% confidence interval for the mean of the entire senior class 2. A sample of 10 measurements of the length of a chip gave a mean of 2.36 cm and a standard deviation of 0.06 em. Find the a. 95% confidence limits b. 99% confidence limits