Chapter 8 Power Point

“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.