Statistics Exam 1 Review

List the 4 properties of a binomial distribution:

- independent trials - fixed number of trials - probability of success remains constant - 2 mutually exclusive outcomes

Probability: a long term relative frequency whose value is between ___ and ___.

0 and 1

Calculate the expected value (mean) of the discrete data given in the frequency table below: x = 0 1 2 3 f(x) = 0.17 0.14 0.36 0.33

formula: µ = ∑x(f(x)) 0(0.17) + 1(0.14) + 2(0.36) + 3(0.33) = 1.85 µ = 1.85

Z

z-score

Figure out if the * * statement is a parameter or statistic: In a national survey of high school students (grades 9-12), *47%* of respondents reported that they had already chosen the college they plan to attend.

statistic; a survey is done on a sample

Figure out if the * * statement is a parameter or statistic: A sample of the first 100 people admitted to the San Diego Comic Con resulted in *32%* who said Superman is their favorite super hero.

statistic; because it is from a sample of the first 100 people

∑

sum of

What is a population?

the complete collection of ALL individuals to be studied.

What is a sample?

a sub-collection of members selected from a population to be studied.

There is an equal chance that apples (A), bananas (B), cherries (C), dragon fruits (D), and elderberry (E) can be picked and they are mutually exclusive. a) Find P(C) b) Find P(C') c) Find P(A or E)

a) 1 / 5 b) 1 / 5 + 1 / 5 = 4 / 5 c) becomes P(A)+P(E) = 1 / 5 + 1 / 5 = 2 / 5

Continuous or Discrete - The acceleration of a car as it goes from 0-60 mph

continuous

Continuous or Discrete - The volume of a sphere

continuous

Continuous or Discrete - The number of Snapchats received in a day

discrete

Continuous or Discrete - The number of limbs on a 2 year old tree is 21

discrete

Variance is measure in no unit of measurement.

False - σ²/s² = units squared

s²

sample variance

Assume the random variable X is normally distributed with a mean of 12 and a standard deviation of 5. Solve: P( 16 < X < 20 )

= .1571 z₁= 16 - 12 / 5 z₁= 4 / 5 z₁= .80 ----> get .7881 from Z-Chart z₂= 20 - 12 / 5 z₂= 8 / 5 z₂= 1.6 ----> get .9452 from Z-Chart z₂ - z₁ = .1571

Assume the random variable X is normally distributed with a mean of 12 and a standard deviation of 5. Solve: P(X>2)

= .9772 z= 2 - 12 / 5 z= -10 / 5 z= -2.00 ----> check your Z-Chart to get .9772

Assume the random variable X is normally distributed with a mean of 12 and standard deviation of 5. Answer P(X<8)

=.2119 z= 8 - 12 / 5 z= -4 / 5 z= -.80 ------> check your Z-Chart to get .2119

Identify the sampling method used: An airline company wants to survey its customers one day, so they randomly select 5 flights that day and survey every passenger on those flights.

Cluster Sample - ALL passengers from SOME flights

For probability, anything less than 5% is likely to happen.

False - anything more than 50% is likely to happen.

Data is skewed if the mean and median are equal

False - if the mean and median are equal, the data is symmetric, or the mean is pulled toward the tail if the data is skewed.

To find the median, you add all the numbers together and divide by the number of entries in the data set.

False - median is putting the numbers in order from least to greatest and finding the middle value.

Z-scores have a mean of 1 and a standard deviation of 0.

False - they have a mean of 0 and a standard deviation of 1.

Which is NOT robust/resistant?

Mean and Mode

What are the given mean and standard deviation of Z-Scores?

Mean of 0 Standard Deviation of 1

Which IS robust/resistant?

Median

Find the "median, mode, mean, range, sample variance, and sample standard deviation" given from the sample data set: 6,4,7,5,3

Median - 5 Mode - no mode Mean - 5 Range - 4 Sample Variance - s²=2.5 Sample Standard Deviation - s=√2.5

Find P(-1.24 < Z < 1.54)

P(z<-1.24)-P(z<1.54) 0.9382 - 0.1075 = .8307

Find the area to the right of 1.53. WITHOUT a calculator.

P(z>1.53) ----> get from z-chart = 0.9370 1-0.9370 = 0.0630

Give the parameter and statistic: The comptroller of Texas wants to know how she will do in the upcoming State election. She hires a consulting firm and they polled 3,150 registered voters. The consulting firm finds that 57% of the polled voters will vote for her. It turns out that after the election she wins with 60% of the vote.

Parameter - 60% / Population - all votes after the election Statistic - 57% / Sample Size - 3150 registered voters

Give the population and sample of the following statement: The research organization contacts 1,500 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.

Population - all 13-17 years olds in US Sample - 1500 teenagers

Give the population and sample of the following statement: The state Department of Transportation wants to know about out-of-state vehicles that pass over a toll bridge with several lanes. A camera installed over one lane of the bridge photographs the license plate of every tenth vehicle that passes through that lane.

Population - all out of state vehicles Sample - every tenth vehicle

Give the population and sample of the following statement: A farmer wanted to learn about the weight of his soybean crop. He randomly sampled 100 plants and weighted the soybeans on each plant.

Population - all soybean plants Sample - 100 soybean plants

Give the population and sample of the following statement: Lucio wants to know whether the food he serves in his restaurant is within a safe range of temperatures. He randomly selects 70 entrees and measures their temperatures just before he serves them to his customers.

Population - food served at restaurant Sample - 70 randomly selected entrees

Give the population and sample of the following statement: Administrators at Riverview HS surveyed 100 of their seniors to see how seniors at the school felt about the lunches offered at the school.

Population - seniors at Riverview HS Sample - 100 seniors at Riverview HS

Ira ran out of time while taking a multiple-choice test and plans to guess on the last 6 questions. Each question has 4 possible choices, one of which is correct. Let X = the number of answers Ira correctly guesses in the last 6 questions. a) what is the probability that he answers exactly 2 questions correctly in the last 6 questions?

Sample Space {0,1,2,3,4,5,6} P(x=2) 6 Cr 2 (0.25)²(0.75)⁴ = = 0.2966

Find the value of Z such that P( Z > z ) = .025

Since we are given the z-score, just look up in the table. 1.0000 - 0.0250 = .9750 .9750 in z chart = 1.96

Identify the sampling method used: A principle orders t-shirts and wants to check to make sure they were printer properly. She checks 5 shirts from all ten boxes of t-shirts that were ordered.

Stratified Sample - SOME t-shirts from ALL boxes.

Identify the sampling method used: A teacher is interested in gathering information. While students are lined up for school pictures, that teacher passes out a survey to every 20th student.

Systemic Sample

A mean can be either a parameter or a statistic.

True

A mean is known as a statistic if it is computed from the sample.

True

A probability of one is certain to occur.

True

A probability of zero is impossible.

True

In probability, anything in between 0 and 1 is possible.

True

Standard deviation is measured in units (for example: centimeters)

True

The correct example of a parameter is µ and σ

True

Z-score is measured in no unit of measurement.

True

The mean and the standard deviation are given for non-standard distributions.

True; X~N(µ,0)-µ², σ are given and Z~N(0,1)-µ = always 0, σ is always 1.

What is Continuous data?

is qualitative data that covers range of values without gaps, interruptions, or jumps; a continuous count of numbers (1, 1.1, 1.2, 1.3...)

What is Discrete data?

is quantitative data that is countable (1,2,3,...)

What skew is mean<median<mode?

left-skewed; small tail to the left, large hump on the right

What is a parameter?

measurement from the population (average) *hint* p-p = population = parameter

What is a statistic?

measurement from the sample *hint* s-s = sample = statistic

Figure out if the * * statement is a parameter or statistic: The department chair was interested in the average test one score for statistics classes. The average score of all the classes was *79%*.

parameter; because it is from a population of all statistics classes

µ

population mean

N

population size

σ

population standard deviation

σ²

population variance

P()

probability

q

probability of failure

p

probability of success

Qualitative or Quantitative - Shapes of candy in a variety pack.

qualitative; not a count or measurement

Qualitative or Quantitative - Zip code

qualitative; not a count, discrete

Qualitative or Quantitative - Number on hockey jersey.

qualitative; not counting

Qualitative or Quantitative - Phone number.

qualitative; not representing a count

Qualitative or Quantitative - Volume, weight, height, time, age.

quantitative; continuous counting/measurement

Qualitative or Quantitative - How many phone calls have you made in the last 24 hours?

quantitative; counting

Qualitative or Quantitative - Number of calories in a donut.

quantitative; it is continuous

What skew is mode<median<mean?

right-skewed; big hump on the left and small tail on the right

s

sample

x⁻ (bar over the x)

sample mean

n

sample size