Estimating Ability with Confidence Intervals

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Presentation transcript:

Estimating Ability with Confidence Intervals

Vocabulary used in this Lesson Margin of Error Confidence Interval Sample Mean Standard Deviation

Confidence Interval An interval of plausible values where an Data point may fall An interval is better than single value because of chances of accuracy have increased

95% Confidence Intervals Three very common intervals: Interval Z-score 90% 95% 99% Interval Z-score

Interpreting Confidence Intervals About 95% of all the intervals we construct will contain the athlete’s ability “We are 95% confident that the interval of plausible values from _________ to _________ contains ____________’s ability ___________________________”

General Form for Confidence Interval

OR Margin of Error Upper Endpoint – Observed Performance Observed Performance – Lower Endpoint

Calculating a Confidence Interval for a Proportion

Calculating a Confidence Interval for a mean

Lawn Weeds A survey of 1898 adults with lawns conducted by Harris Interactive Poll found that 45% of the adults said that dandelions were the toughest weeds to control in their yards. Find the 95% confidence interval of the true proportion who said that dandelions were the toughest weeds to control in their yards.

Lawn Weeds Hence you can say with ______ confidence that the true percentage of adults who consider dandelions the toughest weeds to control in their lawns is between ___________ and _________.

Perry Como Fans Fifty-six percent of respondents to an online poll said that they were Perry Como fans. If 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are Perry Como fans? Estimate at the 95% confidence level.

Perry Como Hence you can say with ______ confidence that the true percentage of________________________________________________________________is between ___________ and _________.

Continue working on examples

KNOCKOUT

1. What are the three most common confidence intervals? 10%, 100% and 1000% 90%, 95% and 99% 80%, 90% and 100% 85%, 95% and 100%

2. What is the only confidence interval we deal with in this course? 100% 99% 95% 90%

3. What is the meaning of 𝑝̂? Ability (true proportion of successes) Performance (observed proportion of successes) Sample size Confidence Interval

4. What is the meaning of 𝑝? Ability (true proportion of successes) Performance (observed proportion of successes) Sample size Confidence Interval