Warm Up: Identify the population and the sample: 1. A survey of 1353 American households found that 18% of the households own a computer.

Transcription

1 Warm Up: Identify the population and the sample: 1. A survey of 1353 American households found that 18% of the households own a computer. 2. A recent survey of 2625 elementary school children found that 28% of the children could be classified obese. 3. The average weight of every sixth person entering the mall within 3 hour period was 146 lb. 1

2 Identify the population and the sample: 1. A survey of 1353 American households found that 18% of the households own a computer. population: all American households sample: collection of 1353 American households surveyed 2. A recent survey of 2625 elementary school children found that 28% of the children could be classified obese. 3. The average weight of every sixth person entering the mall within 3 hour period was 146 lb. population: all elementary school children sample: collection of 2625 elementary school children surveyed sample: every 6th person entering the mall within the 3 hour period population: all people entering the mall within the assigned 3 hour period 2

3 Parameter: A number that describes the population. In statistical practice the value of a parameter is not known, because we cannot examine the entire population. Statistic: A number that can be computed from the sample data without making use of any unknown parameters. In practice, we often use a statistic to estimate an unknown parameter. Samples Statistics Population Parameter 3

4 The average income of the sample of households contacted by the Current Population Survey was $60,528. This number is a statistic because it describes this one sample. The population that the poll wants to draw conclusions about is all 113 million U.S. households. The parameter of interest is the mean income of all of these households. We do not know the value of this parameter. IMPORTANT: SYMBOL REPRESENTATION 4

5 The population mean (if possible) would be the most accurate. Sample means, however, are possible. The problem is they vary. This is called sampling variability. VARIABILITY IS OK!!! 5

6 Thousands of travelers pass through Guadalajara airport each day. Before leaving the airport, each passenger must pass through the Customs inspection area. Customs officials want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light shows, the passenger will be searched by customs agens. A green light means "go ahead" Customs officers claim that the probability that hte light turns green on any press of the button is.70. 6

7 Parameter or Statistic? The ball bearings in a large container have a mean diameter cm. This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have mean diameter cm. Because this is outside the specified limits, the container is mistakenly rejected. 7

8 Parameter or Statistic? The Tennessee STAR experiment randomly assigned children to regular or small classes during their first four years of school. When these children reached high school, 40.2% of spanish speaking students from small classes took the ACT or SAT college entrance exam. Only 31.7% of spanish speaking students from regular classes took one of these exams. 8

9 Parameter or Statistic? The ball bearings in a large container have a mean diameter cm. This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have mean diameter cm. Because this is outside the specified limits, the container is mistakenly rejected. 9

10 Parameter or Statistic? A random sample of female college students has a mean height of 64.5 inches, which is greater than the 63 inch mean height of all adult american women. 10

11 Parameter or Statistic? A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was 125,000 11

12 Parameter or Statistic? The average salary of all assembly line employees at a certain car manufacturer is $33,

13 Parameter or Statistic? The average late fee for 360 credit card holders was found to be $

14 Warm Up: A hotel manager gathered that hotel guests on average run water on average 11.4 minutes per day with a standard deviation of 2.6. What % of shower guests shower more than 12 minutes per day? 14

15 The hotel holds 84 guests, and they are all showering at the the same time. What is the probability that the 84 guests take a shower longer than 12 minutes? 15

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