Statistics 104 – Homework 9
Due Thursday, November 7, 2013
Homework is due on the due date at the end of the lecture.
Reading:
October 29 – November 5
Chapter 7
Assignment:
1. Complete the following problems from the text: 7.7, 7.9, and 7.23.
7.7 Random variability in baseball
7.9 Experimental medication
7.23 Household size
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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 success/failure
(
)
condition,
, is 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.
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c) In a large bag of 176 M&M’s there are 60 blue M&M’s. Is this an unusually
large number of blue M&M’s? Explain.
3. In Bloomberg National Poll conducted September 20 – 23, 2013, 1000 adults selected
at random from all the adults in the United States were asked the question: “Do you
favor or oppose allowing same-sex couples to get married?” As reported on
www.pollingreport.com/civil.htm 55% of those surveyed were in favor, while 36% of
those surveyed were opposed. 9% of those surveyed were unsure. The poll has a
margin of error of plus/minus 3.1 percentage points.
a) What is the population?
b) What is the variable? What kind of variable is it (categorical or numerical)?
c) What is the parameter?
d) What is the sample?
e) Give the number, not a proportion or a percentage, of adults in the sample who
favor allowing same-sex couples to get married.
f) What proportion of the entire U.S. adult population would be in favor of allowing
same-sex couples to get married?
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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) What are the means and standard deviations of these distributions?
Sample size
Mean
16
25
Standard Deviation
c) Sketch in the distribution of the sample mean y for random samples of size 16
and 25 in the spaces provided below.
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