Confidence Intervals

* A confidence interval is created to estimate a population mean or a population proportion.

1-Sample Z Interval for Means…..(avg’s) 1-Sample Z Interval for Proportions…..(%’s)

* N: Name the Interval * A: Assumptions/Conditions * S: Stats from calculator * C: Confidence Interval * A: And * R: Result in Context

* Do you tweet? * How many students in this class have a twitter account? * Do you think that typical high school students are like you? * What percent of all students at Rancho are on twitter?

* Let’s plan a survey at Rancho to determine the proportion of students who use twitter? * How many students should we survey? * How accurate do we want our results? * How can we do a random survey that gives a good representative of the population of students at Rancho?

PER 2

PER 3

* Using your C.I. formula for means, calculate the interval for a sample mean of 26, a sample size of 64, and the population standard deviation is known to be Z* will be for this problem. (25.611,26.389)

* The critical value for Z* can be found on the bottom of the t table in the formula sheets. * Common values for Z* are the following: 90% Confidence……..Z* = % Confidence……..Z* = % Confidence……..Z* = 2.576

After 126 student scores playing Dice Master, Mr. Pines has calculated the sample mean to be 156. Construct a 95% confidence interval to estimate the true mean for playing this game. Assume that the population standard deviation is known to be σ = 55.5 (146.31,165.69) I am 95% confident that the true mean score for Dice Master is between and

(146.31,165.69) 95% confidence interval estimate For this data

Mr. Pines bowling scores over the past 15 years have a mean of 168 and a standard deviation σ = Amazingly he has kept track of 40 scores to calculate these statistics. Calculate the following intervals a)90% b)95% c)99% Now, let’s see what a large sample size will do to our interval, use a 95% Confidence level d) n = 400 e) n = 4000

* A narrow interval is more accurate than a wide interval * Larger sample sizes will shrink your interval(more accurate) * Smaller sample sizes will stretch your interval(less accurate) * A higher confidence level will stretch your interval, for example 99% CI will be wider than a 95% CI. 90% ( ) 95% ( ) 99% ( ) n = 1000 ( ) n = 100 ( ) n = 10 ( )

* As a group, create 1 confidence interval multiple choice type problem. * Give 4 answers to choose from * Make sure to write your question in complete sentences and add context. * Be creative.

Construct a 95% confidence interval

* Interpret this interval in context. (205.05, ) I am 95% confident that the true mean score for students playing Yahtzee is between and

1-Sample Z Interval for Means Assumptions: We have an independent SRS of 15 farkle scores. Our population of scores that our sample was taken from is more than 10 times our sample size. We will assume that our sample is approximately normal. STATS n = 15 σ = 1675 Sample Mean = % Confidence Interval ( 4272, 5695 ) I am 90% confident that the true mean Farkle score is between 4272 and 5695.

Each group took a different SRS of 15 Farkle scores and created a 90% confidence interval. All seven groups intervals captured the true mean score of 4733(revealed at the end of activity)

The mean number of hot dogs eaten each year at a certain contest for the past 30 years is 27. Assume that the population standard deviation is known to be σ = A 95% confidence interval will be constructed. Calculate the margin of error and the standard error.

A shark expert measures the lengths of great white sharks that come within one mile of the coast. How many sharks does she need to measure to have a margin of error of at most 3 feet with 95% confidence? Assume the standard deviation for these types of sharks is known to be 8.23 ft. DON’T BE SCARED So, about 29 sharks

ACTIVITY * Count the total # of beads that are given to your group. * Count the # of beads that are green. * Calculate the proportion of beads that are green. * Construct a 95% confidence interval for the true proportion of green beads in the bucket.

There are 2920 beads in the bucket, 600 of them are green. Which makes the proportion of green beads to be How many of our intervals captured this proportion?

13 out of 14 our our 95% confidence intervals captured the true proportion of green beads.

A Rancho AP statistics student did a large stratified survey of 160 students at Rancho. The question was whether students were upset or not about the school starting earlier for the school year. Of the students surveyed, 113 of them responded, “yes”. Construct and interpret a 98% confidence interval for the true proportion of students at Rancho who are upset about starting school earlier. How many students would we need to survey to have a margin of error of 2% or less with 98% confidence? Assume that the proportion of students that would respond “yes” is the same as the previous question.

Harry and Lloyd are doing a survey of people in the town of Aspen. They are trying to determine the proportion of them who have a pet bird. In their first attempt at the survey 14 people out of 52 responded that they have a pet bird. Construct and interpret a 99% confidence interval. (.11,.43) I am 99% confident that the true proportion of people in Aspen who own a pet bird to be between.11 and.43.

Harry and Lloyd are doing a survey of people in the town of Aspen. They are trying to determine the proportion of them who have a pet bird. In their first attempt at the survey the sample proportion was.27. How many people would they need to survey to have a margin of error of 3% or less with 90% confidence? Assume that the proportion of people who who would say they have owned a pet bird is the still.27 Lloyd, we better ask at least 593 people

* As a group, create 1 confidence interval multiple choice proportions type problem. * Give 4 answers to choose from * Make sure to write your question in complete sentences and add context. * Be creative.