Download Chapter 10 Day 1

CHAPTER 10 DAY 1
Margin of Error
• The estimate is our guess for the value of the unknown
parameter. The margin of error shows how accurate we
believe our guess is, based on the variability of the
estimate.
Confidence Interval
• Gives the estimate ± margin of error.
• And we can state this for a given percentage of
confidence – which we will use a z-score chart for in this
lesson!
Confidence Intervals
• Any confidence interval has two parts: an interval
computed from the data and a confidence level giving
the probability that the method produces an interval that
covers the parameter.
• Usually the confidence interval is 90% or higher because
we want to be quite sure of our conclusions.
• Assume that 37% of all voting fans chose Ohio State to
play in the National Championship game vs. Florida State
with a ±6% error for 95% confidence.
• What is the confidence interval for the percent who
believe that Ohio State belonged?
• What does this mean?
• We can say with 95% confidence that the true percentage of all
fans is between 31%-43%
Confidence Interval
• To get confidence level C we want the central probability
C under a normal curve. To do that, we must go out z*
standard deviations on either side of the mean. The
number z* is the same for any normal distribution.
Critical Values
• The number z* with a probability p lying to its right under
the standard normal curve is called the upper p critical
value of the standard normal distribution.
Confidence Interval
• To compute confidence intervals from a standard normal
curve, we use a tail area…
• For a confidence level of 90%, tail area is .05
• z* = 1.645
• For a confidence level of 95%, tail area of .025
• z* = 1.960
• For a confidence level of 99%, tail area of .005
• z* = 2.576
Confidence Interval for a Population Mean
• Draw an SRS of size n from a population having unknown
mean µ and known standard deviation σ. A level C
confidence interval for µ is
𝑥±
𝜎
∗
𝑧
𝑛
Example
• Bob’s Pizza Shop averages µ pizzas on a Saturday
evening. An SRS of 500 restaurants, σ = 8, averages 103
pizzas and is approximately normal. Determine a 95%
confidence interval for µ.
Homework #5
• The Degree of Reading Power (DRP) is a test of the
reading ability of children. Use the DRP scores for 44
third-grade students in a suburban school district given.
• A. Make a stemplot of the distribution.
• B. Suppose that the standard deviation of the population
of DRP scores is known to be σ = 11. Give a 99%
confidence interval for the mean score in the school
district.