STAT 1350 Lecture Notes - Lecture 19: Confidence Interval, Standard Deviation, Statistic
27 Apr 2018
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3/22/2018
Chapter 21 (Part 2): Confidence Intervals
● Name that Symbol
○ The standard deviation of a sample of test scores is 1.75 points → s
○ The proportion of all astronauts who like science is 1.0. → P
○ The proportion of a sample of OSU students who ride the bus daily is 0.65. →
^p
○ The sample average price of a used car is $1500. → ^x
○ The standard deviation of a population of tree heights is 9.84 feet. → σ
○ The mean weight of all dogs in Columbus is 57.5 pounds → μ
● Review of the Basic Ideas
○ Remember the general format of the confidence interval:
■ Confidence interval = sample statistic ± margin of error
○ Important points to keep in mind:
■ The margin of error, and hence the width of the interval, gets smaller the
as the sample size increases.
■ The margin of error, and hence the width of the interval, increases or
decreases, depending on the confidence level.
■ Saying we are “95% confident” means that 95% of all possible samples
that could be drawn from the population will produce an interval that
covers the true population parameter.
● Top Hat Question
○ Which of the following values will ALWAYS be within the 95% confidence
interval limits?
■ A. The population mean
■ B. The sample size
■ C. The sample mean
■ D. The sample standard deviation
● Interpreting a Confidence Interval
Document Summary
The standard deviation of a sample of test scores is 1. 75 points s. The proportion of all astronauts who like science is 1. 0. The proportion of a sample of osu students who ride the bus daily is 0. 65. The sample average price of a used car is . The standard deviation of a population of tree heights is 9. 84 feet. The mean weight of all dogs in columbus is 57. 5 pounds . Remember the general format of the confidence interval: Confidence interval = sample statistic margin of error. The margin of error, and hence the width of the interval, gets smaller the as the sample size increases. The margin of error, and hence the width of the interval, increases or decreases, depending on the confidence level. Saying we are 95% confident means that 95% of all possible samples that could be drawn from the population will produce an interval that covers the true population parameter.
