Transcript Review

Lesson 8 - R
Chapter 8 Review
Objectives
• Summarize the chapter
• Define the vocabulary used
• Complete all objectives
• Successfully answer any of the review exercises
• Use the technology to compute means, standard
deviations and probabilities of Sampling
Distributions
Vocabulary
• None New
Chapter 8 – Section 1
The sampling distribution of the sample
mean is
1) The standard normal distribution with
mean 0 and standard deviation 1
2) The distribution of sample means
3) The histogram showing the relationship
between the samples and the means
4) The method used to construct simple
random samples
Chapter 8 – Section 1
If a random variable X has a skewed right
distribution, then the distribution of the
sample mean for a sample of size n = 500
for X is
1)
2)
3)
4)
Approximately normal
Very skewed right
Somewhat skewed left
Uniformly spread across its range
Chapter 8 – Section 1
If a random variable X has a standard
deviation σ = 20, then the standard error of
the mean for a sample of size n = 100 is
1)
2)
3)
4)
2
5
20
100
Chapter 8 – Section 2
An example of a problem dealing with
sample proportions is
1) Calculating the mean weight of elephants
2) Calculating the number of customers
arriving at a bank between 1:00 pm and
1:10 pm
3) Calculating the ratio of people’s heights to
their weights
4) Calculating the percent of cars that get
more than 30 miles per gallon
Chapter 8 – Section 2
A study found that 33% of adult females
dye their hair. In a sample of 500 adult
females, what proportion do we expect to
find who dye their hair?
1)
2)
3)
4)
.33 / 500, or approximately .0007
√.33•.67/500 , or approximately .021
.33
.66
Chapter 8 Summary
• The sample mean and the sample proportion
can be considered as random variables
• The sample mean is approximately normal with
– A mean equal to the population mean x  
– A standard deviation equal to  x   / n
• The sample proportion is approximately
normal with
 p̂  p
– A mean equal to the population proportion
– A standard deviation equal to  p̂  p( 1  p ) / n
Summary and Homework
• Summary
– Samples of sample means have the same
means as population, but have tighter
spreads (less variance) than the population
– Samples of sample proportions have the
same proportion as the population, but also
have less variance than the population
• Homework:
– pg 443 – 444; 4, 6, 11, 14
Homework
• 4: sampling distro of x-bar: mean: μ stdev: σ/n
sampling distro of p-hat: mean: p stdev: (p)(1-p)/n
• 6 μ=90 min σ=35 min
a) P(x > 100) = 0.3875
normalcdf(100,E99,90,35)
b) normal, μ = 90 min, σ = 35/10 = 11.068 min
c) P(x-bar > 100) = 0.1831, no
normalcdf(100,E99,90,11.068)
• 11 p = 0.09 n = 200
a) apx normal, μp=0.09, σp= (.09∙.91/200 = 0.0202
b) P(p-hat ≤ 0.06) = 0.0688
normalcdf(-E99,0.06,0.09,0.0202)
c) P(x ≥ 25) = 0.0416, Yes
normalcdf(0.125,E99,0.09,0.0202)
• 14 μ=$443 σ=$175 n=50 σx-bar = $175/50 = $24.7487
P(x > $400) = 0.5970 (not what we are looking for!)
P(x-bar > $400) = 0.9588
normalcdf(400,E99,443,24.75)