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“Miller Lite has 1/3 less calories than regular beer” or so the
commercial says.
According to Miller, a 12 oz Miller Lite has 96 calories
(www.millerlite.com). Suppose that the actual calorie content varies
from bottle to bottle, with a mean of 96 calories and a standard
deviation of 5 calories.
We will sample 48 bottles of Miller Lite, carefully measuring the
calories in each bottle, and report the average number of calories per
bottle for the sample.
Identify the situation.
•What type of population is this? Numerical OR
Categorical
•What information has been given about the
population?
•What information has been given about the
sample to be obtained?
Consider the sample to be obtained…
•What is the mean value of X
• What is the standard deviation of X
• Is a normal distribution appropriate for our X
What is the probability that the sample mean will
be greater than 97.5 calories
If our sample of 48 bottles has an average greater
than 97.5… Would you be surprised? Why or why not?
X
n = 48
i.
Mean Value for
i.
Std Dev of
i.
Is normal?
i.
P( > 97.5)
n = 72
Describe how increasing the sample size affects each of the following
•Mean Value for X
•Standard Deviation of X
•Probability that the value of is far from the mean value X
A mid-size city must decide whether or not to build a new combined bus
and train station. To build the new station will require an increase in city
taxes. According to a city politician, 70% of all city residents support the
tax increase to build a combined bus and train station.
An opinion poll of 1000 city residents will ask whether they favor a rise
in taxes to pay for a combined bus and train station.
Identify the situation.
•What type of population is this? Numerical OR
Categorical
•What information has been given about the
population?
•What information has been given about the
sample to be obtained?
Consider the sample to be obtained…
•What is the mean value of p
• What is the standard deviation of p
• Is a normal distribution appropriate for our p
What is the probability that the sample
proportion will be greater than 0.75?
If more than 75% of the sample support the tax, a referendum
will be introduced in the city’s next election. Is it likely that
the referendum will be on the next ballot? EXPLAIN.