Math 240 - Introduction to Statistics- Sample Midterm test 1 W 2015PROVIDE CALCULATIONS AND REASONING FOR EACH ANSWER. SHOW YOUR WORK.1. (8 marks) According to the freshmen 15 legend, college freshmen gain 15 pounds (or 6.8) kilograms during their freshmen year. Listed below are amounts of weight change (in kilograms) for a simple random sample of freshmen included in the study. Positive values correspond to the students who gained weight and negative to the students who lost weight. Complete the table below and use it for calculations in this problem.Weight gain/loss: 11, 3,0,-2,9, -2.XX2

11121

3

00

-24

9

-24

a. Calculate mean, median and mode. Do these values appear to support the legend that college students gain 15 pounds during their first year of college studies?

b. Determine variance and standard deviation for this data set. Interpret both, variance and standard deviation

c. Calculate and interpret the coefficient of variation for this data set.

2. (12 marks) For a data set the following statistics were determined:

a. Sketch a regular boxplot.

b. By comparing relevant of the above statistics and based on the boxplot comment on skewness of the distribution for this data set.

c. Calculates limits for the mild outliers.________________________________________________________________________________________________________________________________________________________________________________Are there any outliers in this data set? Why?

d. Between what values is the 25% of the highest values? _____________________________________________

e. If assumed the data come from a bell shaped distribution, what percent of all observation fall within three standard deviations of the mean?___________________________f. *If the distribution of the data is unknown within what values fall at least 84% most central observations?________________________________________ (bonus)

3. (12 marks) Listed below are 18 top annual salaries (in millions of dollars) of US TV personalities. 50.0, 42.0, 41.0, 41.0, 38.0, 36.0, 35.0, 27.0, 25.0 15.0, 13.0, 12.0, 10.0, 9.6, 8.4, 6.7, 6.0, 5.8

a) Calculate third quartile

b) What percentile is the value: 27?

c) Calculate and interpret z-score for the observation of 35.0. ______________________________

d) Is 35.0 an unusual observation? Why? ___________________________________________________________________________________________________________________________

e) If you were to divide this data set into classes what would you choose for The number of classes______________Why?____________________________________________ The class width____________________Why?____________________________________________ First class lower class limit____________Why?___________________________________________ Calculate here: first class lower class limit+(number of classes*the class width)____________________________________________

4. Given the relative frequency distribution tableIQ ScoreFrequency

50-692.6%

70-8942.3%

90-10944.9%

110-1299.0%

130-1491.3%

a. Sketch both, the histogram and a relative frequency polygon (on the same graph) for this relative frequency distribution.

b. Does it appear that the data come from normally distributed population? Why?____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. (10 marks) Tossed a symmetrical coin three times.a. Give one example of a simple event________________________________b. Draw a tree diagram for this procedure

c. Determine the probability space:________________________________________________________________________________________

d. What is the probability that obtained three heads?______________________________________________e. What is the probability that obtained at least two tails OR there are both, heads and tails, in an outcome?You may want to draw a Venn diagram as a help in answering this problem.

6. (6makrs) In one of the Albertas public schools districts a survey was conducted on quality of food in the cafeterias in each school. The researchers. From each school the researchers randomly selected the whole classes and distributed a survey to every among all the students. It was up to the students whether they returned the filled out questionnaire to the researchers. What two sampling methods best describe the procedure of sampling in this

problem?___________________________________________________________________________________

What are pros and cons such smapling?________________________________________________________

One of the questions of the questionnaire asked: How would you rate the quality of food on a scale from 1 to 5, where 1=poor and 5=excellent. What level of measurement applies to answers to this questions?_________________________________What measures of central tendency can be found for this data?___________________________________If for all the answers to this questions calculated the mode, is it a statistic or a parameter?_________________

7. Based on the information in the table below answer questions following the table.Guilty PleaPlea of not guilty

Sentenced to prison387

65

Not sentenced to prison561

25

a. If 1 of the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison.

b. It three person are randomly selected find the probability that neither of them was guilty Plea but not sentenced to prison.

c. Find the probability of being sentenced to prison, given the subject entered a plea of not guilty.

d. Find the probability of being sentenced to prison, given a subject entered a plea of guilty.

e. If one of the subject is randomly selected, find the probability of selecting someone who entered a plea of not guilty OR was not sentenced to prison.

f. If one subject was randomly selected out of 1028 subject, find the probability of selecting someone that who was sentenced to prison and entered a guilty plea.

g. If one of the subjects is randomly selected, find the probability of selecting someone who was not sentenced to prison and did not enter a plea guilt.

h. If two different study subjects are randomly selected, find the probability that they both were sentenced to prison.

i. If two different subjects were selected what is the probability that they both entered pleas of not guilty?

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