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# Word Problems: Hypothesis Testing and Confidence Intervals

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1. 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% 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 the days is it expected the machine will be re-calibrated.

2. In an election between two candidates the regular vote count came out in favor of candidate A. When the absentee ballots were counted the percent 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 calculate the P-value to be 0.8. A newspaper writes" this show 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 briefly.

3. When an airline sells tickets for a flight, only about 90% of the people who but the ticket actually show up. (a) For a flight with 400 seats, they can be 95% confident that between ___ and ____ percent of the people will to actually show up. Fill in the blanks with a percentage, (B) approximately how many ticket should they sell so that there is less than a 10% chance they run out of seats

4. Bond investors often like to buy shares in mutual funds that give return that closely follow quotes indices, such as the Lehman Brothers government index. One popular index is computed from 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 points of the index? You can assume bond returns typically vary in range from -5% to +5% with a standard deviation of about 25%. But state any other assumptions you make for this.

5. 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?