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HBX-Business Analytics- Questions and Answers
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HBX-Business Analytics- Questions and Answers
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HBX-Business Analytics- Questions andAnswers
Consider the four outliers in the 2012 revenue data: companies with revenue of $237 billion,
$246 billion, $447 billion, and $453 billion. If we removed these companies from the data set,
what would happen to the standard deviation Correct Ans-The standard deviation would
decrease.
is correct
The standard deviation gives more weight to observations that are further from the mean.
Therefore, removing the outliers would decrease the standard deviation.
A journalist wants to determine the average annual salary of CEOs in the S&P 1,500. He does
not have time to survey all 1,500 CEOs but wants to be 95% confident that his estimate is within
$50,000 of the true mean. The journalist takes a preliminary sample and estimates that the
standard deviation is approximately $449,300. What is the minimum number of CEOs that the
journalist must survey to be within $50,000 of the true average annual salary? Remember that the
z-value associated with a 95% confidence interval is 1.96.
Please enter your answer as an integer; that is, as a whole number with no decimal point.
Correct Ans-The formula for calculating the minimum required sample size is n≥(z*s/M)^2,
where M=50.000 is the desired margin of error for the confidence interval, s=$449,300 is the
sample standard deviation, and z=1.96. Using these data we find that
1.96449,30050,0002=310.201.96449,30050,0002=310.20 Since n must be an integer (let's not
even think of what 0.20 CEOs would look like!) and n must be greater than or equal to 310.20,
we must round up to 311. Since 310.20 is closer to 310 than to 311, we would normally round
310.20 down to 310. However, in this case we must round up to find the smallest integer that
satisfies the equation. Therefore, the minimum required sample size is 311.
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