Post on 03-Apr-2015
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JeopardyJeopardyLet’s Let’s
Test ItTest ItI’mI’m
NormalNormal
I RegressI RegressAnalyzeAnalyze
ThisThis
#’s Where#’s Where
do theydo they
come fromcome from
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With With
ConfidenceConfidenceProbablyProbably
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Final JeopardyFinal JeopardyMake your bidsMake your bids
What is another name for a young bear What is another name for a young bear cub that is ready to leave home? cub that is ready to leave home?
The answer isThe answer is
BRUINBRUIN
Data ProductionData Production
A researcher in early childhood education believes A researcher in early childhood education believes that kindergarten-age children are more receptive that kindergarten-age children are more receptive to help from a female teacher. The researcher to help from a female teacher. The researcher randomly samples four classes with male teachers randomly samples four classes with male teachers and four classes with female teachers. The and four classes with female teachers. The students in the classes are interviewed, and a students in the classes are interviewed, and a measure of how receptive the students in each measure of how receptive the students in each class are to help from the teacher is determined. class are to help from the teacher is determined. This study is an example of This study is an example of
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AnswerAnswer
Observational Observational studystudy
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QuestioQuestionn
Data AnalysisData Analysis
Find the mean of the Find the mean of the following test scores following test scores
18, 19, 15, 12, 2118, 19, 15, 12, 21
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AnswerAnswer
1717
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QuestioQuestionn
Correlation & Correlation & Regression Regression
Is your social security number Is your social security number a categorical or quantitative a categorical or quantitative
variable?variable?
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categoricalcategorical
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QuestioQuestionn
What part of Normal What part of Normal
don’t you understand?don’t you understand?
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68, 95, 99.7 is called the ____rule
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QuestioQuestionn
emperical
Tests ofTests of
SignificanceSignificance
When doing a t test, if the P When doing a t test, if the P Value is < .05 then we would Value is < .05 then we would ______ the null hypothesis and ______ the null hypothesis and
______ the alternative.______ the alternative.
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Reject, acceptReject, accept
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QuestioQuestionn
ProbabilityProbability
Randy is a 70% free throw Randy is a 70% free throw shooter, if he takes 40 shots, shooter, if he takes 40 shots,
about how many will he about how many will he make?make?
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QuestioQuestionn
2828
ConfidenceConfidenceIntervalsIntervals
As your level of confidence As your level of confidence increases, the confidence increases, the confidence
interval gets _______. interval gets _______.
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WiderWider
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QuestioQuestionn
Data ProductionData Production
A biologist is studying the effect of nutrients and levels of A biologist is studying the effect of nutrients and levels of salinity in water on the growth of fish. Ten fish are to be salinity in water on the growth of fish. Ten fish are to be assigned at random to each of 12 similar tanks in a controlled assigned at random to each of 12 similar tanks in a controlled environment. The biologist wants to use 4 different nutrients environment. The biologist wants to use 4 different nutrients and 3 different salinity levels. In this design, how many units and 3 different salinity levels. In this design, how many units are being assigned to each treatment? are being assigned to each treatment?
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QuestioQuestionn
1212
Data AnalysisData Analysis
Find QFind Q11 and Q and Q33 for the for the following test scores show following test scores show without using a calculatorwithout using a calculator
18, 19, 15, 12, 2118, 19, 15, 12, 21
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AnswerAnswer
13.5 and 2013.5 and 20
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QuestioQuestionn
Correlation & Correlation & RegressionRegression
$200$200A ________ variable measures an A ________ variable measures an
outcome of a study. outcome of a study.
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AnswerAnswer
responseresponse
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QuestioQuestionn
What part of Normal What part of Normal
don’t you understand?don’t you understand?
Find z with a test score of 85, if Find z with a test score of 85, if test scores have a normal test scores have a normal
distribution of N(80, 2)distribution of N(80, 2)
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AnswerAnswer
z = 2.5z = 2.5
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QuestioQuestionn
Tests ofTests of
Significance Significance
For a two sided t test the t test For a two sided t test the t test statistic is 2.1 with df = 18, find statistic is 2.1 with df = 18, find
the P Valuethe P Value
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AnswerAnswer
.05.05
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QuestioQuestionn
ProbabilityProbability
The price of gasoline increased The price of gasoline increased from $3.70 per gallon to from $3.70 per gallon to
$3.95 per gallon in the last $3.95 per gallon in the last three months. What percent three months. What percent
increase is this?increase is this?
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QuestioQuestionn
6.7%6.7%
ConfidenceConfidence
Intervals Intervals
A significance level of A significance level of αα = .05 = .05 has upper tail probability of has upper tail probability of
____________
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AnswerAnswer
.025.025
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QuestioQuestionn
Data ProductionData Production
You would like to compare shopping tendencies for You would like to compare shopping tendencies for different age groups and ethnicities. You go to different age groups and ethnicities. You go to Wal-Mart and ask questions to different people. Wal-Mart and ask questions to different people. This type of sampling is called ______________.This type of sampling is called ______________.
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Convenience Convenience samplingsampling
Data AnalysisData Analysis$300$300
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Find the IQR for the ages of children in a family
15, 14, 12, 19
44
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QuestioQuestionn
Correlation & Correlation & RegressionRegression
$300$300What is the difference between r What is the difference between r
and rand r²²
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QuestioQuestionn
R tells you how related R tells you how related to variables are. Rto variables are. R² tells ² tells you how well a regression you how well a regression
fits the datafits the data
What part of Normal What part of Normal don’t you understand?don’t you understand?
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Find the area to the right of z = 1.27
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AnswerAnswer
1 - .898 = .102
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QuestioQuestionn
Tests ofTests of Significance Significance
What is a type I and a type II errorWhat is a type I and a type II error
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AnswerAnswer
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QuestioQuestionn
Type I – Reject Ho when Ho is true
Type II – Accept Ho when we should
reject.
ProbabilityProbability
55% of adults drink coffee55% of adults drink coffee Draw a venn Draw a venn diagramdiagram
25% drink tea25% drink tea What % drink only soda?What % drink only soda?
45% drink soda45% drink soda
15% drink coffee and tea15% drink coffee and tea
5% drink all three5% drink all three
25% drink coffee and soda 25% drink coffee and soda
5% drink only tea5% drink only tea
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ConfidenceConfidenceIntervalsIntervals
Hillary and Obama are running for president, Hillary and Obama are running for president, you want a determine the you want a determine the minimum sample minimum sample sizesize with 95% confidence and a margin of with 95% confidence and a margin of
error of 3%. (Assume probability of getting error of 3%. (Assume probability of getting any one vote is .5)any one vote is .5)
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QuestioQuestionn
z*(sqrt p (1-p)/n) z*(sqrt p (1-p)/n) << .03 .03
n = 1067n = 1067
Data ProductionData Production
Name three things that Name three things that must be satisfied when must be satisfied when designing a question for designing a question for
a survey.a survey.
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QuestioQuestionn
No undercoverage, No undercoverage, No bias, a SRSNo bias, a SRS
Data AnalysisData Analysis
What is the Acronym used to What is the Acronym used to describe the collection of describe the collection of
data, mostly used in normal data, mostly used in normal distributionsdistributions
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CUSS or SUCSCUSS or SUCS
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QuestioQuestionn
Correlation & Correlation & RegressionRegression
In Florida, as the number In Florida, as the number powerboat registrations increase, powerboat registrations increase, the number of manatees killed the number of manatees killed increases by y=-35.2 + .113b. increases by y=-35.2 + .113b. Predict the number of manatees Predict the number of manatees killed when 500 boats were killed when 500 boats were registered.registered.
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AnswerAnswer
2222
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QuestioQuestionn
DAILY DOUBLEDAILY DOUBLE
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QuestioQuestionn
What part of Normal What part of Normal
don’t you understand?don’t you understand?
Draw a picture of a Normal distribution Draw a picture of a Normal distribution with N(34,5) distributionwith N(34,5) distribution
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QuestioQuestionn
Tests ofTests ofSignificanceSignificance
Explain the law of large Explain the law of large numbers numbers
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As the number of As the number of observations drawn from observations drawn from a population increases, a population increases,
the sample mean the sample mean approaches the true approaches the true
population meanpopulation mean
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ProbabilityProbability
What is the probability of flipping a What is the probability of flipping a coin 3 times and getting exactly 2 coin 3 times and getting exactly 2 heads?heads?
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QuestioQuestionn
3/8 or .3753/8 or .375
ConfidenceConfidenceIntervalsIntervals
What is the formula for a What is the formula for a confidence interval for a two confidence interval for a two
samplesample
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xx11 – x – x22 ± t* s± t* s11²/n²/n11 + s + s22²/n²/n22
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Data ProductionData Production
A university wants to know how much A university wants to know how much money students earn from summer money students earn from summer employment out of a population of employment out of a population of 22,100 undergraduates. Explain how 22,100 undergraduates. Explain how you would choose a stratified random you would choose a stratified random sample.sample.
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Students are broken up Students are broken up by levels, male and by levels, male and
female and by students female and by students level of financial aid. A level of financial aid. A SRS is drawn from each SRS is drawn from each
group.group.
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QuestioQuestionn
Data AnalysisData Analysis
Find the standard deviation for the following test Find the standard deviation for the following test scores show without using a calculatorscores show without using a calculator
18, 19, 15, 12, 2118, 19, 15, 12, 21
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Sqrt( (18-17)Sqrt( (18-17)² + ² + (19-(19-17)17)² + ² + (15-17)(15-17)² ² (12-17)(12-17)² ²
(21-17)(21-17)²²
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QuestioQuestionn
Correlation & Correlation & RegressionRegression
Log y = .2 + . 3xLog y = .2 + . 3x
Transform the data into an exponential equation Transform the data into an exponential equation
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QuestioQuestionn
y = (10^.2)(10^.3x)y = (10^.2)(10^.3x)
y = 1.58y = 1.58·2^x·2^x
What part of Normal What part of Normal
don’t you understand?don’t you understand?
Suppose that the percent of all Suppose that the percent of all Americans between 15-24 that have Americans between 15-24 that have been in a car accident is normally been in a car accident is normally distributed with N(.7, .03) distribution. distributed with N(.7, .03) distribution. In a sample of 2300 Americans, what In a sample of 2300 Americans, what is the probability that less than 65% is the probability that less than 65% have been in a car accident.have been in a car accident.
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P(Z < P(Z < .65 - .7.65 - .7 ) ) .03 .03
= -.05/.03 = - 5/3 = = -.05/.03 = - 5/3 = P(z < -1.67) = .0475 P(z < -1.67) = .0475
or 4.5%or 4.5%
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QuestioQuestionn
Tests ofTests ofSignificanceSignificance
A local teachers’ union claims that the average A local teachers’ union claims that the average number of school days missed due to illness by number of school days missed due to illness by the city’s school teachers is fewer than 5 per the city’s school teachers is fewer than 5 per year. A random sample of 28 city school teachers year. A random sample of 28 city school teachers missed an average of 4.5 days last year, with a missed an average of 4.5 days last year, with a sample standard deviation of 0.9 days. Assume sample standard deviation of 0.9 days. Assume that “days missed” follow a normal distribution that “days missed” follow a normal distribution with mean μ. with mean μ.
Estimate the Estimate the PP-value-value using your table using your table
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Between .005 Between .005 and .0025and .0025
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QuestioQuestionn
ProbabilityProbability
What is the difference between What is the difference between a binomial distribution and a a binomial distribution and a
geometric distribution?geometric distribution?
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Binomial – has n Binomial – has n observations with observations with probability pprobability pGeometric – has probability Geometric – has probability of p for success and 1-p for of p for success and 1-p for failure, n is the number failure, n is the number failures until the first failures until the first successsuccessExample: Find the probability of flipping Example: Find the probability of flipping
a coin 7 times and getting 3 heads. a coin 7 times and getting 3 heads. Find the probability of flipping coin 4 Find the probability of flipping coin 4 times, and stopping once you flip heads.times, and stopping once you flip heads.
ConfidenceConfidenceIntervalsIntervals
Is there a difference between the mean Is there a difference between the mean summer earnings for male and female summer earnings for male and female college students? Give a 90% confidence college students? Give a 90% confidence interval for the difference between the interval for the difference between the mean summer earnings of male and mean summer earnings of male and female students.female students.
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GroupGroup nn xx ss
MalesMales 675675 $1884.52$1884.52 $1368.37$1368.37
FemaleFemale 621621 $1360.39$1360.39 $1037.46$1037.46
Yes. ($413, $634)Yes. ($413, $634)
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QuestioQuestionn
Data ProductionData Production
Using your calculator to generate Using your calculator to generate random integers. How would you random integers. How would you simulate a 70% free throw shooter. simulate a 70% free throw shooter. That takes 12 free throws in a game.That takes 12 free throws in a game.
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randInt(0,9,12)->L1randInt(0,9,12)->L1The numbers 0-6 would represent a The numbers 0-6 would represent a shot made the numbers 7,8,9 would shot made the numbers 7,8,9 would
represent a miss. Find the proportion represent a miss. Find the proportion in 12 numbersin 12 numbers
Data AnalysisData Analysis
Name 3 ways to measure Name 3 ways to measure the spread of datathe spread of data
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Standard Standard deviation, range, deviation, range,
and IQRand IQR
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QuestioQuestionn
Correlation & Correlation & Regression Regression
In the equation y = 1.0892 + .189xIn the equation y = 1.0892 + .189x
The variable y tells us how much gas is The variable y tells us how much gas is used (cubic feet), the variable x tells used (cubic feet), the variable x tells us how many days in one month a us how many days in one month a family uses their heater. Interpret family uses their heater. Interpret the slope of the regression line.the slope of the regression line.
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QuestioQuestionn
On average, each On average, each additional day using additional day using
the heater, the heater, predicts .189 more predicts .189 more
cubic feet of gas per cubic feet of gas per day.day.
What part of Normal What part of Normal
don’t you understand?don’t you understand?
Find P(-1.13 < Z < 2.16)Find P(-1.13 < Z < 2.16)
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P(z < -1.13) = .1292P(z < -1.13) = .1292P(z < 2.16) = .9846P(z < 2.16) = .9846
Therefore Therefore P(-1.13 < Z < 2.16)P(-1.13 < Z < 2.16)
= .9846 - .1292 = .8554= .9846 - .1292 = .8554
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QuestioQuestionn
Tests ofTests of
SignificanceSignificance $600$600
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AnswerAnswer
The SAT scores of entering freshmen at X University have a normal distribution N(1200,90), while the SAT scores of entering freshmen at Y University have a normal distribution with N(1215, 110). Independent random samples of 100 freshmen are selected from each university. The probability that the sample mean from X University exceeds the sample mean from Y University is
85.54%
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ProbabilityProbability
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Kobe Bryant is an 84% free throw shooter. In game 2 against the nuggets he scored 49 points and rolled up Carmelo and K Mart(in), in the game he made 8 out of 9 free throws. Find the probability of that happening. (binomial distribution)
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QuestioQuestionnBinomcdf(n,p,k) Binomcdf(n,p,k)
Binomcdf(9,.84,8) Binomcdf(9,.84,8) = =
.79.79
DAILY DOUBLEDAILY DOUBLE
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QuestioQuestionn
ConfidenceConfidence
IntervalsIntervals $600$600
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AnswerAnswer
Are jet ski’s dangerous? The Are jet ski’s dangerous? The regression equation is 327.29 regression equation is 327.29 + .0048x, t = 21.079, df = 8 + .0048x, t = 21.079, df = 8 Calculate and interpretCalculate and interpret a 98% CI for a 98% CI for the true slope of the regression line. the true slope of the regression line. (The slope is the increase in number (The slope is the increase in number of jet ski accidents per year per of jet ski accidents per year per thousand)thousand)
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QuestioQuestionn
(.0042, .0054) With 98% (.0042, .0054) With 98% confidence, we estimate that confidence, we estimate that for every extra thousand jet for every extra thousand jet skis in use, the number of skis in use, the number of accidents increase by a accidents increase by a
mean of 4.2 to 5.4 per year.mean of 4.2 to 5.4 per year.