all problems 1 of BIT EXHIBIT 2 Growing a Family A previous semester survey on t

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1 of BIT EXHIBIT 2 Growing a Family A previous semester survey on the number of siblings each student had in his family revealed an average of 2.78 kids per family, counting the answering students. Surveys families at random and ask that same question tend to find lower averages (of roughly 2.0 children per family). Question Offer some explanation as to the difference between the average found in the previous semester survey (typical number, by the way) and the average that general surveys often find. 1. EXHIBIT 3 Bully Folly On October 4, 1994, the San Francisco Examiner went to press with the headline "1 in 4 Youths Abused, Survey Finds." The telephone survey of 2,000 children ages 10-16 asked in part: "in the past year have you been slapped, kicked, punched, hit, or threatened with an object by an adult, sibling, or another child." Questions 1. Give at least one reason the headline is deceptive and suggest a better one. ia What role does the Margin of Error play, if any, in quantifying the confusion in this exhibit? 2. 202 BEYOND THE NUMBERS 2.26

Explanation / Answer

Exhibit-2:

Solution-1. There could be multifold reason of fall in the average no. of kids per family as follows:

1) The survey is based on just sample not the entire population. These family considered for both sampling survey might have varied that resulted in difference since it is a random sampling.

2) Although the definition of "kids" based on Age range etc is not given, over the semester these kids might have grown and are found to be no more "kids".

Exhibit-3:

Answer-1: The headline concludes about entire population based on sample survey without statistically testing using Hypothesis testing for proportion. Sample gives just indication that has to tested statistically.

The better headline should be:

"About 25% youths prone to abuse, survey indicates"

Answer-2: For concluding the firm result of hypothesis testing, we need sample size that comes from 'Margin of Error' using following equation:

Sample size n = (z*Sigma/Margin of Error)^2

where z is quantile of standard normal distribution which is 1.96 for 95% confidence &

Sigma is standard deviation

Thus, it is clear that, if Margin of Error increase, the allowable sample size decreases.

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