Northeastern University Week 2 Standard Error Statistics Questions

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4. A stock index fund invests in a very large number of different stocks, so the return you get from it is roughly the average return for the stocks in the index. (a) Which of these two choices would give you a better chance of tripling your money within a month: investing all your money in the index fund, or investing all your money in a few randomly chosen stocks that make up the index? (b) Which of these two choices would give you a better chance of losing almost all of your money within a month: investing all your money in the index fund, or investing all your money in a few randomly chosen stocks that make up the index? 22. Twenty-five independent polls of one thousand random people each are taken during the course of an extremely close election campaign. People in the poll are asked which of the two candidates they favor and the percentage who favor the incumbent candidate is computed for each poll. (a) estimate the standard error and the margin of error for each of these polls. Justify your answer, and briefly explain the difference between them. (b) How large a poll sample would be required if a margin of error of only 10% was desired? (c) One of the other candidate’s approval rating averaged around 48% over all the twenty-five polls. If you computed the standard deviation of the list of all twenty-five poll percentages for this candidate, approximately what number would you expect to get? Explain. 28. Bond investors often like to buy shares in mutual funds that give returns that closely follow commonly quoted indices, such as the Lehman Brothers Government Index. One popular index is computed form several thousand different bond types. Roughly how many bonds do you think would be needed in a portfolio that could reliably give one-year portfolio returns within half a percentage of the index? You can assume bond returns typically vary in range from -5% to +5% with a standard deviation of about 2.5%, but state any other assumption you make for this. 17. Reports from a new system set up to monitor Internet use by company employees indicate that 145 out of a random sample of 1100 employees at a corporation accessed Internet sites that were clearly not related to their jobs over the last week. On average, employees who accessed non-job related sites spent 4.8 hours per week at such sites with a standard deviation of 2.1 hours. a. Give a 95% confidence interval for the percentage of employees at the corporation who accessed non-job related sites. b. Briefly explain in on short sentence how to interpret this interval. C. Statistics show that about 10% of people nationwide access non-job related sites at work. Is this company really any different from the national statistics? d. Can we say that roughly 95% of people at this company spent in the range of 4.8 hours plus or minus 4.2 hours on non job related web sites? 20. When an airline sells tickets for a flight, only about 90% of the people who buy a ticket actually show up. a. For a flight with 400 seats, the airline can be 95% confident that between ______ and _____ percentage of the people will actually show up. Fill in the blanks with a percentage. b. Approximately how many tickets should they sell so that there is less than a 10% chance they run out of seats? 28. From historical data you know that the time it takes to do a certain job is normally distributed with a mean of 130 minutes and a standard deviation of 20 minutes. To monitor performance, each week a sample of 25 jobs is selected and the average time it takes to do the job is recorded. In a particular week the average time to do the job was 128 minutes with a standard deviation of 16 minutes. The distribution of times in the sample comes out bellshaped. What can you say, if anything about each of the following intervals: a. 128 ± x 16 b. 130 ± 2 x (20/√25) c. 128 ± 2 x (16/√25) d. 128 ± 2 x (20/√25) 11. A manufacturer of cereal has a machine that , when working properly, puts 20 ounces of cereal on average into a box with a standard deviation of 1 ounce. Every morning workers weigh 25 filled boxes. If the average weight is off by more than 1 percent from the desired 20 ounces per box, company policy requires them to re-calibrate the machine. In a sample of 100 days where the machine is working properly all day, on how many of the days is it expected the machine will be re-calibrated? 13. In an election between two candidates the regular vote count came out in favor of Candidate A. When the absentee ballots were counted, the percentage in favor of Candidate B was so high that B came out ahead overall. Someone conducts a statistical test to see how rare such a difference between the two vote counts would be just by chance and calculated the pvalue to be .08. A newspaper writes “this shows that there is roughly a 92 percent chance that the difference between the two counts is due to some irregularity other than simply chance alone”. Do you agree with the newspaper’s interpretation of the p-value? Explain. Question X. Where do CFOs get their money news? According to Robert Half International, 47% get their money news from newspapers, 15% get it from communication/colleagues, 12% get it from television, 11% from the Internet, 9% from magazines, 5% from radio, and 1% don’t know. Suppose a researcher wants to test these results. She randomly samples 67 CFOs and finds that 40 of them get their money news from newspapers. Does the test show enough evidence to reject the findings of Robert Half International?
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Running head: MANAGERIAL STATISTICS

MANAGERIAL STATISTICS:
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MANAGERIAL STATISTICS

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4. A stock index fund invests in a very large number of different stocks, so the return you
get from it is roughly the average return for the stocks in the index.
(a)
Which of these two choices would give you a better chance of tripling your money
within a month: investing all your money in the index fund, or investing all your money in
a few randomly chosen stocks that make up the index?
The choice that would give a better chance of tripling the money is the second choice which
entails investing all the money in a few randomly chosen stocks that make the index since one
will be able to select stocks that offer high returns rather than an index fund that averages the
return of the stocks.
(b)
Which of these two choices would give you a better chance of losing almost all of
your money within a month: investing all your money in the index fund, or investing all
your money in a few randomly chosen stocks that make up the index?
The second choice of investing all the money in a few randomly chosen stocks that make up the
index fund gives a better chance of losing almost all of the money within a few month since, the
risk associated with this choice is not diversified as that of investing in an index fund.
22. Twenty-five independent polls of one thousand random people each are taken during
the course of an extremely close election campaign. People in the poll are asked which of
the two candidates they favor and the percentage who favor the incumbent candidate is
computed for each ...


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