Have Yourself a Merry Statistical Christmas
1. Happy the Elf has been hard at work making toys. Over the past 3 weeks, he has the following daily totals: 43, 50, 52, 46, 45, 51, 60, 44, 40, 43, 47, 49, 52, 46, 44, 45, 48, 49, 44, 46, 42
a) Create a Histogram of Happy’s daily toy output. Comment on its shape, center, and spread.
b) Use our definition of outlier to determine if 60 is an outlier.
c) At Santa’s workshop, a typical elf’s daily toy output is approximately normal with a mean of 41 with a standard deviation of 4. Find Happy’s mean toy output for the last 3 weeks and calculate what percentile that places him in in respect to the other elves.
2. One of this year’s gifts from Santa’s Workshop is a dollhouse. Each dollhouse has 10 working lights throughout the house. Based on past experience, 1% of the light bulbs in each large case that they order to make the dollhouses are defective. Instead of testing the entire box, they just grab 10 bulbs and, if any are defective, then they replace them. An elf grabs 10 bulbs for the next house. What is the probability that all 10 work?
3. Joey thinks he figured out Santa’s lists. His research suggests that 70% of all kids are for the most part good, and the rest are naughty. Of all the good kids, 1% accidentally get placed on the “Naughty List”. Of the naughty kids, 50% do some last minute good deed and get moved to the “Nice List”.
a) What is the probability that a randomly selected kid will get a lump of coal this year?
b) What is the probability that a randomly selected kid was good given that he was on the “Nice List”?
4. Smiley Elf has an idea that he wants to try out. He believes that changing the color of their uniform might help increase productivity. (Lets face it, red and green for 100’s of years may be getting old.) He comes up with 3 other color combinations: Blue and gold, Silver and Black, and Yellow and orange. Somehow, he has convinced 120 other elves to help him out. Design an experiment that will help Smiley see if uniform color effects productivity.
5. Over the years, the number one injury at Santa’s workshop is thumb injuries. Since World War II, new safety training in hammering has been part of every new elf’s orientation. The number of thumb injuries for given years are listed here.
|
Year |
1950 |
1970 |
1990 |
2000 |
2010 |
|
# of Thumb Injuries |
1052 |
845 |
660 |
520 |
460 |
a) Create a scatterplot of the data. What is its correlation?
b) Write the LSRL. Use it to estimate the number of thumb injuries in 1960.
c) Interpret the slope in the context of the problem.
d) Calculate r-squared and interpret it in the contest of the problem.
