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Published bySusanna Dorsey Modified over 2 years ago

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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**

What is the standard deviation of Is a normal distribution appropriate for our

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**What is the probability that the sample mean will be greater than 97**

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 Mean Value for Std Dev of Is normal? P( > 97.5)

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**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.

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Objectives (BPS chapter 11) Sampling distributions Parameter versus statistic The law of large numbers What is a sampling distribution? The sampling.

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