“miller lite has 1/3 less calories than regular beer” or so the commercial says
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“Miller Lite has 1/3 less calories than regular beer” or so the commercial says. - PowerPoint PPT PresentationTRANSCRIPT
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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.
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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?
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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
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What is the probability that the sample mean will be greater than 97.5 calories
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If our sample of 48 bottles has an average greater than 97.5… Would you be surprised? Why or why not?
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n = 48 n = 72
i. Mean Value for
i. Std Dev of
i. Is normal?
i. P( > 97.5)
XX
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X
X
X
Describe how increasing the sample size affects each of the following•Mean Value for
•Standard Deviation of
•Probability that the value of is far from the mean value
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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.
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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?
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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
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What is the probability that the sample proportion will be greater than 0.75?
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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.