Statistics 104 – Homework 9
Due Thursday, March 29, 2012
Homework is due on the due date at the end of the lecture.
Reading:
March 20 – March 27
Chapter 7
Assignment:
1. Complete the following problems from the text: 7.7, 7.10, 7.11, 7.23, 7.24, 7.29, and
7.30.
2. The maker of M&M’s says on its website that 24% of Milk Chocolate M&M’s are
blue. Suppose that M&M’s are packaged at random. We wish to examine the sample
proportion of blue Milk Chocolate M&M’s, p̂ , in various sized bags.
a) For each of the different sized bags, give the mean and standard deviation of the
sampling distribution of p̂ . Also comment on whether or not the conditions are
met for the sampling distribution to be approximately normal.
i) Fun size bags containing 18 M&M’s.
ii) Small size (1.69 oz) bags containing 56 M&M’s
iii) Medium size (3.27 oz) bags containing 108 M&M’s
iv) Large size (5.3 oz) bags containing 176 M&M’s
v) Party size (42 oz) bags containing 1400 M&M’s
b) For a large bags containing 176 M&M’s, use the 68-95-99.7 Rule to describe how
the sample proportion of blue M&M’s might vary from bag to bag.
c) In a large bag of 176 M&M’s there are 58 blue M&M’s. Is this an unusually
large number of blue M&M’s? Explain.
3. In an NBC News/Wall Street Journal poll conducted between February 29 and March
3, 2012, 800 adults selected at random from all the adults in the United States were
asked the question: “Do you favor or oppose allowing gay and lesbian couples to
enter into same-sex marriages?” As reported on www.pollingreport.com/civil.htm
49% of those surveyed were in favor, while 40% of those surveyed were opposed.
11% of those surveyed were unsure or answered “Depends”. The poll has a margin
of error of plus/minus 3.5 percentage points.
a)
b)
c)
d)
e)
What is the population?
What is the variable? What kind of variable is it (categorical or numerical)?
What is the parameter?
What is the sample?
Give the number, not a proportion or a percentage, of adults in the sample who
favor same-sex marriages for gay and lesbian couples.
f) What proportion of the entire U.S. adult population would be in favor of same-sex
marriages for gay and lesbian couples?
1
4. Below is a screen shot of the web page that simulates sampling from a population
with a quantitative/numerical variable.
a) Describe the shape of the black population distribution.
b) Sketch in the distribution of the sample mean y for random samples of size 16
and 25 in the spaces provided below.
c) What are the means and standard deviations of these distributions?
Sample size
Mean
16
25
Standard Deviation
2