STATS

PROBLEM 1

In a research to know the methodology used by sure begun (undertaken) Quebecers for the analysis and the evaluation of the quality of the various projects which are subjected to them, we put 8 questions in each of sixty companies retained for this study.

Q1: does the company make a detailed analysis of the projects which are subjected to him (her)?

1. No (2) Yes

Q2: has the company a textbook (manual worker) of procedures?

1. No (2) Yes

Q3: how do you consider the quality of the made analyses?

1. Excel
2. Very good
3. Average
4. Weak (Weakness)
5. Bad

Q4: does the company plan to modify its approach (initiative)? (1) No (2) Yes

Q5: according to you, what is the utility of the feasibility studies?

1. Very useful
2. Very useful
3. Averagely useful
4. Little useful

Q6: what is the figure of business of the company (in thousand dollars)?

1. < 100
2. 100-500
3. 501-1 000
4. > 1 000

Q7: according to you, what is the evolution of the company with regard to its business sector?

1. Similar Growth
2. Fast Growth
3. Less fast Growth
4. Diminution

Q8: what is the working time which the company dedicates on examination of the files which are subjected to him (her)?

The answers to these questions by sixty enterprises are summarized in the picture (board) 1.1

1. Specify, for each of the composed questions, the scale (ladder) of used measure.
2. Make a perusal of the data of the questions 1 and 3. Summarize then the results (profits) in the form of tables (absolute frequencies and percentages).
3. Present the results (profits) obtained for one of the nominal variables by means of a diagram with circular sectors.
4. Present the results (profits) obtained for an ordinal variable by means of a diagram with vertical bars

5) We want to analyze the data associated with the question 8 according to the annual turnover of the company. For every category of following statistics concerning the variable working time, determine:

1. The duration averages of work dedicated on examination of files
2. The median
3. The interval interquartile, Q3-Q1

6) We want to build the histogram and the polygon of frequencies for the same variable "working time".

1. Determine the number of necessary classes by using the rule of Sturges and calculate then their amplitudes.
2. Build the picture (board) of the classes, the absolute frequencies and the accumulated frequencies.
3. Build the histogram and the polygon of the frequencies.

7) We want to know if 60 companies having participated in the study are fully qualified teachers ISO9002 or not and we wish to know the cost of this certification. The picture (board) summarizes 1.2 us the situation.

1. Estimate the proportion of companies which are ISO-certified 9002
2. Determine a reliable interval to 95 % for the real proportion of company which (who) are ISO-certified 9002.
3. Which is the statistical margin of error in the estimation of the real proportion for the level of specified confidence (trust) in 7 b)
4. Determine the average cost of this certification, its variance and his (her) distance-type (-chap).
5. Determine the relative variation of this cost.
6. Determine a reliable interval to 95 % for the real average cost associated with this certification.

G) Which is the statistical margin of error in the estimation of the average cost of certification for the specified level of confidence in 7 f)

1. The picture (board) 2.2 presents the distribution of the amounts of money spent by every referee on the purchase of jeans during the last 12 months. What measures of central trend (tendency) allows summarizing indeed this distribution (casting)?

1. On average, how much every category of referees such spent on the purchase of jeans during the previous year?
2. Globally, questioned 50 % of the persons spent an amount upper to what value?
3. Making him (it) needed to know which size (cutting) of jeans carried (wore) the young people. The picture (board) 2.3 presents the answers of the poll (sounding) realized for that purpose. From the point of view of the making, would it be useful to know average size (cutting) of the carried (worn) jeans?

1. How can we use the information supplied by the picture (board) 2.3 to plan its own production according to the sizes?
2. Making him (it) wants to know also the type (chap) of stores where the young people buy their jeans; the picture (board) 2.4 presents the compilation of the answers to this question. What measure of central trend (tendency) is the most useful?
   
3. For every category of referees, what type (chap) of stores is the most frequented for the purchase of jeans? Globally, the answer is the same?
4. If this young person's sample is representative 130 000 students (boys and filles0 of the collective level in Quebec, which is the approximate amount of money (silver) these did they spend during the last 12 months on the purchase of jeans?

PROBLEM 3

In a factory, a single machine is used to pour some flour into labeled bags «500 g ". The weight X some flour which is paid (poured) can obviously vary a little bag to the other one. However, the machine can be settled (adjusted) so that the random (unpredictable) variable X distributes according to a normal law of average and standard deviation 2, 5 g. We can also suppose that the quantity of flour paid (poured) into a bag is independent from that paid (poured) into quite other bag.

An inspector of a governmental agency visits the factory to make sure that the regulations (payments) on the labeling are respected well. He (it) takes at random 20 bags among those who have just been filled (performed) by the machine and he (it) weighs the contents of each by means of a very precise balance. The one two just has to weigh less than 500 g so that he (it) emits (utters) a report of nonconformity.

1. If the machine is settled (adjusted) so that the paid (poured) average quantity is equal to what is indicated on the bag, what is the probability that the inspector expresses an opinion of nonconformity?
2. In how much should be settled (adjusted) the average to reduce to 5 % at least the probability so that a report of nonconformity is emitted (uttered)?
3. Supposing that the machinery is settled(adjusted) so that the average is equal to the quantity calculated there b) and so that the inspector decides to verify 40 bags rather than 20, which is then the probability so that he observes at least a bag containing less than 500 g of flour?
4. Supposing that the machinery is settled(adjusted) so that the average is equal to the quantity calculated in 2) and so that 4 800 bags are a day performed, so that do we know about the total quantity of flour paid(poured) into these bags?
5. Supposing that the machinery is settled (adjusted) so that the average is equal to the quantity calculated in 2), which is the probability that at least one of 4 800 bags filled (performed) in a day contains less than 500 g of flour?

PROBLEM 4

Hawaii account 770 000 inhabitants among whom 60 % are Asian, 39 % are whites and 1 % are black.

We pull (fire) at random a sample of 7 persons.

1. What is the probability to obtain a majority of Asiatic?
2. What is the probability that we obtain no black?
3. What is the number hoped by Asiatic in the sample? What is its standard deviation?

Price: $48.17

Solution: The downloadable solution consists of 27 pages, 2117 words and 20 charts.
Deliverable: Word Document