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) Approximately normal

2) Very skewed right

3) Somewhat skewed left

4) 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

2) 5

3) 20

4) 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) .33 / 500, or approximately .0007

2) √.33•.67/500 , or approximately .021

3) .33

4) .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– A standard deviation equal to

• The sample proportion is approximately normal with– A mean equal to the population proportion – A standard deviation equal to

x

pp̂ n/)p(pp̂ 1

nx /

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 mina) P(x > 100) = 0.3875 normalcdf(100,E99,90,35)

b) normal, μ = 90 min, σ = 35/10 = 11.068 minc) P(x-bar > 100) = 0.1831, no normalcdf(100,E99,90,11.068)

• 11 p = 0.09 n = 200a) apx normal, μp=0.09, σp= (.09∙.91/200 = 0.0202b) 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)