Statistics
Download
1 / 49

Statistics - PowerPoint PPT Presentation


  • 145 Views
  • Uploaded on

Statistics. 5.2. Quiz 6. A quick quiz consists of a true/false question followed by a multiple-choice question with four possible answers ( a,b,c,d ). An Unprepared student makes random guesses for both answers. a. What is the probability of that both answers are correct

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Statistics' - kane


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Quiz 6
Quiz 6

A quick quiz consists of a true/false question followed by a multiple-choice question with four possible answers (a,b,c,d). An Unprepared student makes random guesses for both answers.

a. What is the probability of that both answers are correct

b. Is guessing a good strategy?


Random variables
Random Variables

Everyone look at figure 5-1 on page 204 of our book.

  • A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure


Random variables1
Random Variables

Everyone look at figure 5-1 on page 204 of our book.

  • A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure

  • A probability distribution is a description that gives the probability for each value of the random variable. It is often expressed in the format of a graph, table, or formula.


Random variables2
Random Variables

Everyone look at figure 5-1 on page 204 of our book.

  • A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure

  • A probability distribution is a description that gives the probability for each value of the random variable. It is often expressed in the format of a graph, table, or formula.


Random variables3
Random Variables

  • A discrete random variable has either a finite number of values or a countable number of values.


Random variables4
Random Variables

  • A discrete random variable has either a finite number of values or a countable number of values.

  • A continuous random variable has infinitely many values, and those value can be associated with measurements on a continuous scale without gaps or interruptions.


Random variables5
Random Variables

  • A discrete random variable has either a finite number of values or a countable number of values.

  • A continuous random variable has infinitely many values, and those value can be associated with measurements on a continuous scale without gaps or interruptions.


Random variables6
Random Variables

Determine whether the given random variable is discrete or continuous.

a. The total amount in (ounces) of soft drinks that you consumed in the past year.

b. The number of cans of soft drinks that you consumed in the past year.

c. The number of movies currently playing in U.S. theaters.

d. The running time of a randomly selected movie.

e. The cost of making a randomly selected movie.


Random variables7
Random Variables

We use probability histograms to graph a probability distribution


Random variables8
Random Variables

We use probability histograms to graph a probability distribution


Random variables9
Random Variables

Requirements for a Probability Distribution

1. where x assumes all possible values.

2. for every individual value of x


Random variables10
Random Variables

Requirements for a Probability Distribution

1. where x assumes all possible values.

2. for every individual value of x.


Random variables11
Random Variables

Based on a survey conducted by Frank N. Magid Associates, Table 5-2 lists the probabilities for the number of cell phones in use per household. Does the table below describe a probability Distribution?


Random variables12
Random Variables

Does (where can be 0, 1, 2, 3, or 4) determine a probability distribution?


Random variables13
Random Variables

Does (where can be 0, 1, 2, 3, or 4) determine a probability distribution?


Random variables14
Random Variables

Does (where can be 0, 1, 2, 3, or 4) determine a probability distribution?


Random variables15
Random Variables

Mean, Variance, and Standard Deviation

  • Mean for a probability distribution


Random variables16
Random Variables

Mean, Variance, and Standard Deviation

  • Mean for a probability distribution

  • Variance for a probability distribution


Random variables17
Random Variables

Mean, Variance, and Standard Deviation

  • Mean for a probability distribution

  • Variance for a probability distribution

  • Variance for a probability distribution


Random variables18
Random Variables

Mean, Variance, and Standard Deviation

  • Mean for a probability distribution

  • Variance for a probability distribution

  • Variance for a probability distribution

  • Standard Deviation for a probability distribution


Random variables19
Random Variables

Mean, Variance, and Standard Deviation

  • Mean for a probability distribution

  • Variance for a probability distribution

  • Variance for a probability distribution

  • Standard Deviation for a probability distribution

    Lets do example 5 in excel!, and then do problem 3 on the worksheet


Random variables20
Random Variables

Determine whether the following is a probability distribution and if so find its mean and standard deviation . Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (0+ denotes a positive probability value that is very small)


Random variables21
Random Variables

Determine whether the following is a probability distribution and if so find its mean and standard deviation . Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (0+ denotes a positive probability value that is very small)


Random variables22
Random Variables

Determine whether the following is a probability distribution and if so find its mean and standard deviation . Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (0+ denotes a positive probability value that is very small)


Random variables23
Random Variables

Determine whether the following is a probability distribution and if so find its mean and standard deviation . Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (0+ denotes a positive probability value that is very small)


Random variables24
Random Variables

Round off rule for

Round results by carrying one more decimal place than the number of decimal places used for the random variable x. If the values of x are integers, round to one decimal place.


Random variables25
Random Variables

Round off rule for

Round results by carrying one more decimal place than the number of decimal places used for the random variable x. If the values of x are integers, round to one decimal place.

Recall the range rule of thumb


Random variables26
Random Variables

Round off rule for

Round results by carrying one more decimal place than the number of decimal places used for the random variable x. If the values of x are integers, round to one decimal place.

Recall the range rule of thumb


Random variables27
Random Variables

Round off rule for

Round results by carrying one more decimal place than the number of decimal places used for the random variable x. If the values of x are integers, round to one decimal place.

Recall the range rule of thumb


Random variables28
Random Variables

Round off rule for

Round results by carrying one more decimal place than the number of decimal places used for the random variable x. If the values of x are integers, round to one decimal place.

Recall the range rule of thumb


Random variables29
Random Variables

Use the range rule of thumb to identify a range of values containing the usual number of peas with green pods. Based on this is it unusual to get only one pea with a green pod? Explain.


Random variables30
Random Variables

Rare Event Rule for Inferential Statistics

If, under a given assumption(such that a coin is fair), the probability of a particular observed event (such as 992 heads in 1000 tosses of a coin) is extremely small, we conclude that the assumption is not correct.


Random variables31
Random Variables

Rare Event Rule for Inferential Statistics

If, under a given assumption(such that a coin is fair), the probability of a particular observed event (such as 992 heads in 1000 tosses of a coin) is extremely small, we conclude that the assumption is not correct.

  • Unusually high number of successes: x successes among n trials is an unusually high number of successes if the probability of x or more successes is unlikely with a probability of 0.05 or less.


Random variables32
Random Variables

Rare Event Rule for Inferential Statistics

If, under a given assumption(such that a coin is fair), the probability of a particular observed event (such as 992 heads in 1000 tosses of a coin) is extremely small, we conclude that the assumption is not correct.

  • Unusually high number of successes: x successes among n trials is an unusually high number of successes if the probability of x or more successes is unlikely with a probability of 0.05 or less.

  • Unusually low number of successes: x successes among n trials is an unusually low number of successes if the probability of x or fewer successes is unlikely with a probability of 0.05 or less.


Random variables33
Random Variables

Rare Event Rule for Inferential Statistics

If, under a given assumption(such that a coin is fair), the probability of a particular observed event (such as 992 heads in 1000 tosses of a coin) is extremely small, we conclude that the assumption is not correct.

  • Unusually high number of successes: x successes among n trials is an unusually high number of successes if the probability of x or more successes is unlikely with a probability of 0.05 or less.

  • Unusually low number of successes: x successes among n trials is an unusually low number of successes if the probability of x or fewer successes is unlikely with a probability of 0.05 or less.


Random variables34
Random Variables

a) Find the probability of getting exactly 3 peas with green pods .

b) Find the probability of getting 3 or fewer peas with green pods.

c) Which Probability is relevant to determine whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b).

d) Is 3 and unusually low number of peas with green pods? Why or why not?


Random variables35
Random Variables

a) Find the probability of getting exactly 3 peas with green pods . 0.023

b) Find the probability of getting 3 or fewer peas with green pods.

c) Which Probability is relevant to determine whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b).

d) Is 3 and unusually low number of peas with green pods? Why or why not?


Random variables36
Random Variables

a) Find the probability of getting exactly 3 peas with green pods . 0.023

b) Find the probability of getting 3 or fewer peas with green pods. 0.027

c) Which Probability is relevant to determine whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b).

d) Is 3 and unusually low number of peas with green pods? Why or why not?


Random variables37
Random Variables

a) Find the probability of getting exactly 3 peas with green pods . 0.023

b) Find the probability of getting 3 or fewer peas with green pods. 0.027

c) Which Probability is relevant to determine whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b). Part (b)

d) Is 3 and unusually low number of peas with green pods? Why or why not?


Random variables38
Random Variables

a) Find the probability of getting exactly 3 peas with green pods . 0.023

b) Find the probability of getting 3 or fewer peas with green pods. 0.027

c) Which Probability is relevant to determine whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b). Part (b)

d) Is 3 and unusually low number of peas with green pods? Why or why not? Yes since


Random variables39
Random Variables

Expected Value

The expected value of a discrete random variable is denoted by E, and it represents the mean value of its outcomes. It is obtained by finding the value of


Random variables40
Random Variables

Expected Value

The expected value of a discrete random variable is denoted by E, and it represents the mean value of its outcomes. It is obtained by finding the value of


Random variables41
Random Variables

You are considering placing a bet on the number 7 in roulette or red for roulette.


Random variables42
Random Variables

  • If you bet $5 on the number 7 in roulette, the probability of losing $5 is 37/38 and the probability making a net gain of $175 is 1/38. Let’s find the expected value if you bet on 7.


Random variables43
Random Variables

  • If you bet $5 on the number 7 in roulette, the probability of losing $5 is 37/38 and the probability making a net gain of $175 is 1/38. Let’s find the expected value if you bet on 7.


Random variables44
Random Variables

  • If you bet $5 on red, the probability of losing $5 is 20/38 and the probability making a net gain of $5 is 18/38. Let’s find the expected value if you bet on red.


Random variables45
Random Variables

  • If you bet $5 on red, the probability of losing $5 is 20/38 and the probability making a net gain of $5 is 18/38. Let’s find the expected value if you bet on red.


Homework
Homework!!!

  • 5-2: 1-17 odd ,21, 25, 27


ad