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Law of Averages

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13. People in a large population average 60 inches tall. You will take a random sample and will be given a dollar for each person in your sample who is over 65 inches tall. For example if you sample 100 people and 20 turn out to be over 65 inches tall, you get $20. Which is better: a sample of size 100 or a sample of size 1,000? Choose one and explain. Does the law of averages relate to the answer you give? In this case a sample size of 100 would be better. This can be explained using law of averages and also by looking at the formula for Margin of Error. ME = 2 * SD of population/SQRT(size of sample) In this case, the SD of population would remain the same. The only factor or value changing is the sample size. Sample size of 100 would …show more content…

If the population average were in fact 8.2 days it is difficult to reasonably expect a sample average to be 4 standard errors above the population average by chance. Thus we reject the null hypotheses and conclude that the average number of days absent for 40 selected random employees would be 12 or more. 3. Market researchers would like to know if customers prefer a well-known brand over a generic brand of soft drink… The interpretation here with p = 0.02 means that if researchers ran a similar test to see if customers prefer a generic brand over a well-known brand, they would have 0.02 (2%) chance of getting results at least as convincing as what these researchers got. 18. A candidate must gather at least 8,000 valid signatures on a petition before the deadline in order to run in an election… According to the information provided, 80% of valid signatures are required (8000 out of 10,000). Let’s formulate our hypotheses around this i.e. Null hypotheses: 20% or more of available signatures are not valid or invalid. Alternate hypotheses: Less than 20% of available signatures are invalid. Let us use α= 0.05 or 5% We are given that out of the

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