1. An automobile manufacturer has problems with sticking accelerator pedals. They have come up with what they believe is a solution to the problem, but to test it exhaustively, they must try it in one sample of all possible configurations of their non-hybrid models. There are ten models, each available in three engine sizes, with two transmission types (manual and automatic) and two drive sides (left-hand drive and right-hand drive). If the company must test one vehicle of each possible configuration, how many vehicles do you test?
2. A study is made of how long a certain brand of light bulbs last under typical use. Data were collected on a sample of 30 bulbs used in a variety of contexts. The data measured how long the bulbs lasted to the nearest month.
24 36 4 40 16 5 18 48 71 69 56 8 12 72 3 72
79 78 3 28 54 4 18 6 30 60 67 73 14 3
a.) Draw a stem-and-leaf display for these data, being careful to label the diagram appropriately.
b.) Calculate the sample mean, sample median, 10% trimmed mean, and 20% trimmed mean for these data.
c.) Calculate the sample range and sample standard deviation for these data.
d.) Draw a histogram of these data, being careful to use proper labels. If you desire, you can use software to do this.
3. In a small company of 10 employees, their current weekly salaries are $500, $280, $370, $460, $320, $250, $620, $480, $290, and $300. Starting next month, everyone in the company will receive a ten percent raise. Since these are the complete data for the entire company, calculate the statistics below as population statistics not sample statistics.
a.) Calculate the mean, median, range, variance, and standard deviation for this population of salaries at the current salary levels.
b.) Calculate the new mean, median, range, variance, and standard deviations once the salaries are raised.
c.) By how many percent did the mean, median, range, variance, and standard deviation increase, and do you expect these results would generally apply to situations where a uniform raising or lowering of observations were to occur?
4. You wish to compare the amounts of money (in Euros) that American tourists spend on visits to the cities of Venice, Rome, and Paris. These data are as follows:
Venice: 234 ?250?225?263?319?221?304?163?271?268?332?229?116?190?280?333?216?375?284?161
Rome: 324?238?206?315?225?372?293?199?192?334?270?375?326?356?284?225?305?333?420?483?307?266?308?341?369?367?255?242
Paris: 312?202?488?203?408?426?459?300?360?451?289?278?565?229?216?523?469?372?306?396?276?283?278?272
a.) Are there outliers in any of the three data sets?
b.) Construct comparative boxplots (one above the other) for the three samples.
c.) Discuss in words how the three samples compare based on your consideration of the boxplots. Consider in particular the center and the spread of the data.
5. The professor in a certain course requires the students to turn in two term papers during the semester. The length of the first paper is supposed to be "about 15 pages", but the professor further explains that what he means by that is that it must be somewhere between 13 and 17 pages. (Since we will measure the length of papers only to the nearest page, this means the first paper can be 13, 14, 15, 16, or 17 pages long.) The second paper must be "about 30 pages in length" meaning somewhere between 27 and 33 pages (27, 28, 29, 30, 31, 32, or 33). For any given student, we express the length of the two papers as an ordered pair (1st paper length, 2nd paper length). Consider that event A is that the second paper is at least twice as long as the first. Event B is that the sum of the lengths of the two papers is less than or equal to 42 pages. Event C is that the sum of the lengths of the two papers is greater than or equal to 48 pages. If an experiment is selecting one student at random and finding the length of his papers, express the solution space S of the experiment as a set of outcomes, and similarly express events A, B, and C as sets of outcomes.