Statistics Semester 1 Final

1. number of malpractice lawsuits a doctor has been involved in the last 3 years

2. quantitative

3. medical doctors in New York

An insurance company wants to know the proportion of medical doctors in New York involved in at least malpractice suit in the last three years. They survey a random sample of 200 medical doctors in New York

1. What is the variable

2. qualitative (descriptive ie. counting or measuring something) or quantitative (values for which operations like addition make sense/numerical response)

3 implied population

population

measurements are taken from EVERY individual of interest, whereas a sample only takes measurements from some of the individuals of interest

sample

only takes measurements from some of the individuals of interest

ordinal

level of measurement suitable for putting data into categories (ie. ratings, scales)

interval

which level of measurement is achieved if the data values can be subtracted from each other, but there is no inherit zero from which measurements begins (ie. years, temp, time of day)

nominal

level of measurement by name only

ratio

there is an inherent zero in the measurements ie. age, scores on tests, amount of something)

stratified sampling

sampling technique where you take SOME from all (Like a buffet)

simple random

sampling technique where you use a random number table to randomly pick

convenience

BAD sampling method where you choose spur of moment on no significant day

systematic

sampling method where you start at a random point, then select every Kth element

1. Identify objects of interest

2. Specify variables and protocols

3 Determine use of population or sample / sample method

4. Collect data

5. Use descriptive and inferential data

6. Note concerns

the 6 basic guidelines for planning a statistical study

census

measurements or observations from the ENTIRE population or area you are looking at

experiment

treatment is deliberately imposed on topic of interest

sample

measurements or observations from a part of the population

simulation

a process by which the actual individuals of a study are replaced by some technological program ie. computer program

selecting people for a study that allows people of interest to be chosen. It prevents researcher bias on the study

what is randomization and why is it helpful to randomize treatments during an experiment

repeating an experiment to verify results and reduces the possibility that results occurred due to chance

what is replication and why is it helpful in an experiment

frequency polygon

this graph begins and ends with a frequency of 0 and the points are plotted using ordered pairs of (class midpoint, class frequency)

stem and leaf plots

the digits of this graphs data are divided in to two parts, leftmost and rightmost

ogive

this graph displays cumulative frequencies as the y coordinates and the graph is useful for determining the number of data values above or below a specified value.

pareto chart

this graph is a specialized bar graph where categories are arranged by frequency in descending order

stem-and-leaf plot

the key of this graph describes the place values of the digits in the graph

circle graph

safe from misinterpretation and shows division of a total quantity and labeled with corresponding percentages

time plots

graph showing data measurements in chronological order

100-36= 64%

George took a test and scored in the 36th percentile. What percentage of the scores were above his score?

4/ 4+6 = 2/5

A student committee is made up of 4 women and 6 men. One of the women is president of the committee. A member of the committee is selected to go see the principal

What is the probability that a women is selected?

6/ 4+6= 3/5

A student committee is made up of 4 women and 6 men. One of the women is president of the committee. A member of the committee is selected to go see the principal

What is the probability that a man is selected?

(5)(2)(7)= 70

You have a choice of 5 different club heads, graphite or steel shafts, and 7 different grips. How many different club selections can he order?

P16,6 = 5765760

Given a class of 10 boys and 6 girls, find each of the following

The distinct number of ways to arrange 6 students in a line

C 16,4 = 1820

Given a class of 10 boys and 6 girls, find each of the following

The distinct number of groups of 4 that can be formed?

C 10,2 X C 6,3

Given a class of 10 boys and 6 girls, find each of the following

The distinct number of groups containing 2 boys and 3 girls?

discrete

variable that can only take a finite number of values usually a whole number

continuous

a variable that can take any of a countless number of values

mu=np=50(.12)= 6 games

A coach found that about 12% of all hockey games end in overtime. WHAT IS THE EXPECTED NUMBER of games ending in overtime if a RANDOM SAMPLE OF 50 hockey games are played?

standard deviation= square root (npq)

how to find standard deviation ( of a BINOMIAL distribution)

mu= 1/p

how to find the expected number in a GEOMETRIC distributionin

1) Draw normal dist. curve and label mean(middle)

2) Go up to 3 spaces as many standard deviations there are

3) use empirical rule to find %

.15 -- 2.35 -- 13.5 -- 34

4) find mu=(n)(standard dev.)= 40(0.25)

Assuming that the heights of boys in a high school basketball tournament have a mean of 70 in. and a standard dev. of 2.5 in, how many boys in a group of 40 in the tournament are taller than 75 inches?

normalcdf (-4,2.81,0,1)

Find P(z<2.81)

'

normalcdf( 1.4,4,0,1)

Find P(z>1.4)

normalcdf(.6,1.12,0,1)

Find P(0.6

invNorm(.98,0,1)

Find the z-score so that 98% of the data lies to the left of z.

normalcdf(-2.2,5,6.7,2.2)=.2198

the length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean of 6.7 minuets and a standard dev. of 2.2 mins.

What is the probability that it will take 5 mins or LESS to assemble a door?

normalcdf(5,7,6.7,2.2)=.3344

the length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean of 6.7 minuets and a standard dev. of 2.2 mins.

What is the probability that it will take between 5 and 7 mins to assemble a door?

1) take 100%-5% = .95

2) invNorm (.95, 32,258, 1005 ->stand dev.)

the 2011 Chicago cubs had an average attendance of 37,258 people with a stand. dev. of 1,005 people. What is the minimum attendance for the 5% of their games that had the highest attendance?

1) x (given)

2) P(x) (given)

3) L1 x L2 // add and this is our mu

4) L1-L3

5) L4 squared

6) L5 x L2 // add and find stand dev. so square root it!

how to find the mean and the standard dev. of the probability distribution