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1 Displaying Data - Solutions 1 Suppose a medical researcher compares the average blood pressures of women who take oral contraceptives to the blood pressures of women who do not. a. Is blood pressure a categorical variable or a quantitative variable and which graph(s) would be most appropriate to use to display the data? Quantitative; we would measure blood pressure. If we categorized the values (e.g. low, medium, high) then this would be a categorical variable. Best graphs would be histogram, boxplot, or stem and leaf b. Is oral contraceptive use (or not) a categorical variable or a quantitative variable and which graph(s) would be most appropriate to use to display the data? Categorical; data produced from yes/no questions are categorical. Best graphs would be pie chart or bar chart c. What variables that affect blood pressure might confuse the comparison of average blood pressures for users and nonusers? That is, what factors affecting blood pressure might differ for users and nonusers. users and nonusers?

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Penn State - STAT - 200

Probabilityhttp:/onlinecourses.science.psu.edu/stat200/book/export/html/28ProbabilityIntroductionLearning objectives for this lesson Upon completion of this lesson, you should be able to do the following: determine which general probability rules to a

Penn State - STAT - 200

Probability Terminology and Notation Terminology Probability: The likelihood that some outcome occurs. The range of any probability is from 0 to 1. The most common calculation of this value comes from the proportion of times that the outcome would occur i

Penn State - STAT - 200

Probability - Solutions 1 Situation: The High School and Beyond data is from a large-scale longitudinal study conducted by the National Opinion Research Center (1980) under contract with the National Center for Education Statist ics. Below is a table repr

Penn State - STAT - 200

Probability Distributionshttp:/onlinecourses.science.psu.edu/stat200/book/export/html/34Probability DistributionsIntroductionLearning objectives for this lesson Upon completion of this lesson, you should be able to: distinguish between discrete and co

Penn State - STAT - 200

Situation I: Find P(X x) 1. Convert x to z-score by z = (x mean)/SD 2. Now find cumulative probability P(Z z) using either the table or Minitab 3. This cumulative probability is the answerSituation II: Find P(X x) 1. Convert x to z-score by z = (x mean)/

Penn State - STAT - 200

1. Suppose that a student needs to buy 6 books for her history course. The number of books that she will be able to find used is a binomial random variable X with n = 6 and p = 0.30. What is the probability that she will find more than 2 used books? P(X>2

Penn State - STAT - 200

Use software for the following problem. 1. Suppose that a student needs to buy 6 books for her history course. The number of books that she will be able to find used is a binomial random variable X with n = 6 and p = 0.30. In other words, the probability

Penn State - STAT - 200

Probability Distributions - Solutions1 In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is binomial or not AND (3) if it is binomial, give values for n and p. a. Number of times a head is flipped in 10 flips o

Penn State - STAT - 200

1 part d: This was discrete but not binomial. There are two outcomes (win/lose), the probability of success is the same for each ticket (or trial) 1/10, and this is independent form one trial to the next (the probability of winning is same whether you won

Penn State - STAT - 200

1 Suppose that State College police department want to estimate the true proportion of all underage drinking among all PSU students. They have come to the statistics department for help with this study. To make the estimation, we randomly asked n = 400 PS

Penn State - STAT - 200

Sampling Distributionshttp:/onlinecourses.science.psu.edu/stat200/book/export/html/42Sampling DistributionsIntroductionLearning objectives for this lesson Upon completion of this lesson, you should be able to: determine the standard error for the samp

Penn State - STAT - 200

Sampling Distributions Solutions1 Suppose that medical researchers want to estimate the true proportion of all teenagers with high blood pressure whose blood pressure would decrease if they took calcium supplements. To test this, they plan a clinical tri

Penn State - STAT - 200

Confidence Intervalshttp:/onlinecourses.science.psu.edu/stat200/book/export/html/46Confidence IntervalsIntroductionLearning objectives for this lesson Upon completion of this lesson, you should be able to: Correctly interpret the meaning of confidence

Penn State - STAT - 200

Confidence Intervals Proportion and One Mean1 The term sampling frame refers to the group that actually had a chance to get into the sample. Ideally, this is the same as the population of interest, but sometimes it isnt. In the following situation, descr

Penn State - STAT - 200

3 6.Use the Standard Normal Table to find the following probability for X = Student Heights for which the mean is 66 inches and the standard deviation is 2 inches: P(X > 69) A) 0.9332 B) - 0.0668 < > C) 0.0668 D) 0.8531 E) 0.1469 F)-0.1469 A lternate Met

Penn State - STAT - 200

Unit Quiz 01https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=433E57EB0D76.Points Awarded Points Missed Percentage8.00 2.00 80.0%1. Decide if the sample is representative (or not) of the population for the question of interest.

Penn State - STAT - 200

Unit Quiz 01https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=433E57EB0D76.Points Awarded Points Missed Percentage8.00 2.00 80.0%1. Decide if the sample is representative (or not) of the population for the question of interest.

Penn State - STAT - 200

Unit Quiz 02https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=C2134DB024A.Points Awarded Points Missed Percentage17.00 1.00 94.4%1. Click the following link Minitab Data or Excel Data. From this data, use software to answer the

Penn State - STAT - 200

Unit Quiz 02https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=C2134DB024A.Points Awarded Points Missed Percentage16.00 2.00 88.9%1. Click the following link Minitab Data or Excel Data. From this data, use software to answer the

Penn State - STAT - 200

Unit Quiz 03https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=74F41B758B0.Points Awarded Points Missed Percentage12.00 3.00 80.0%1. Decide if the probability described is a subjective (personal) probability or a relative freque

Penn State - STAT - 200

Unit Quiz 03https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=74F41B758B0.Points Awarded Points Missed Percentage13.00 2.00 86.7%1. In the past five years, only 5% of pre-school children did not improve their swimming skills af

Penn State - STAT - 200

Unit Quiz 04https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=FA12CE6394B.Points Awarded Points Missed Percentage15.00 1.00 93.8%1. Suppose that a student needs to buy 10 books for her history course. The number of books that s

Penn State - STAT - 200

Unit Quiz 04https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=FA12CE6394B.Points Awarded Points Missed Percentage12.00 4.00 75.0%1. Suppose that a student needs to buy 6 books for her history course. The number of books that sh

Penn State - STAT - 200

Unit Quiz 05https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=A60882BCEC1.Points Awarded Points Missed Percentage10.00 1.00 90.9%1. When a random sample is to be taken from a population and a statistic is to be computed, the st

Penn State - STAT - 200

Unit Quiz 05https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?entryId=A60882BCEC1.Points Awarded Points Missed Percentage8.00 3.00 72.7%1. Which of the following statements is true about a parameter and a statistic for samples taken fr

Penn State - STAT - 200

Unit Quiz 06https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?en.Submitted by LUNBURG, ERIK (exl5087) on 10/7/2010 12:57:06 AM Points Awarded Points Missed Percentage 10.00 5.00 66.7%1. Which theorem or law is correct for supporting the

Penn State - STAT - 200

Unit Quiz 06https:/cms.psu.edu/Section/Assessment/Question/GradeDelivery.aspx?ent.Points Awarded Points Missed Percentage13.00 2.00 86.7%1. Which theorem or law is correct for supporting the notion that as sample size increases the distribution of the

Penn State - STAT - 200

Complement, Independence, Mutually Exclusive Complement and Mutually Exclusive Consider a course where, if completed, you can receive one of the following letter grades: A, B, C, D, or F and each has an equal probability of occurring. That is, P(A) read p

Penn State - STAT - 200

All confidence intervals follow the same formula: Sample Statistic +/- Multiplier*Standard Error For example in problem 7.25 on page 343 since we are talking about a 95% confidence interval to estimate a population mean the above formula would consist of:

Penn State - STAT - 462

Finding P-values For hypothesis testing for proportions were we calculate a Z test statistic (Ill call it Zstat) and for testing means we use a t test statistic (Ill call it tstat). Finding the p-value (or probability value) is based on the alternative hy

Penn State - STAT - 500

Probability Independence and Test of Two Categorical Variables The idea of independence between two categorical variables may sound familiar as we spoke of independence when we discussed probability. Recall that in that lesson we stated that two events, c

Penn State - STAT - 500

Variances, N vs N-1 (1995) Seal.<- file 95varqn.html -> . divide by N or N-1 for variance? Seal =David Seal, 06 Nov 1995=ssm, .From: dseal@armltd.co.uk (David Seal)Newsgroups: sci.math.num-analysis,sci.math,sci.stat.mathSubject: Re: What's Standard D

Penn State - STAT - 200

SOLUTIONS TO ACTIVITY SET 8Activity 8.1 Suppose the amount students at PSU spent on textbooks this semester is a normal random variable with mean = $360 and standard deviation = $90.a. Use the empirical rule for bell-shaped data to determine intervals t

Penn State - STAT - 462

Solution to Homework 1 The following data were collected for a class of 20 students on reading readiness stanines (X) at the end of kindergarten and reading achievement stanines (Y) at the end of first grade. You want to examine how well the readiness sco

Penn State - STAT - 462

Solution - Homework 2 Use the data from Homework 1 to complete this assignment and regress Y on X and store the residuals. 1. Create boxplots for both X and Y. Are there any outliers? No outliers identified. See boxplot below.Box pl ot of X, Y0 X 2 4 Y

Penn State - STAT - 462

Homework 3 - Solutions Covers Chapters 5 and 6 Matrix Methods 1. Using the data for Homework 1 and 2, write in proper matrix form, the matrices for Y, and X. 3 1 1 3 5 4 7 6 7 8 Y = 5 2 7 6 9 8 4 6 9 7 1 1 1 1 1 1 1 1 1 1 X = 1 1 1 1 1 1 1 1 1 1 2 2 1 1 3

Penn State - STAT - 462

Homework 4 Covers Chapters 7 Use the Project Talent data set. 1. Perform a multiple regression by regressing Math on Gender, SES, Sociability, Reading, and Mechanical Reasoning entering the predictors in this order. a. What is the interpretation of the t-

Penn State - STAT - 462

Homework 5 Covers Chapter 8 Use the Project Talent data set. The variable School Size is interpreted as follows: 1 = number of students is less than 100 2 = number of students is from 100 to 399 3 = number of students is 400 or more 1. A lack-of-fit test

Penn State - STAT - 462

Homework 6 Covers Chapters 9 and 10 Use the High School and Beyond (HSB) data set. The data is explained in the HSB Read Me file. USE MATH AS PREDICTOR 1. Some researchers feel an interaction exists between Gender and Writing ability. Create an Gender*Wri

Penn State - STAT - 500

STAT500 HW#2_solutionsSolutions to Homework 2 1) (fifth) a) A=cfw_6 n(A) / n(S) = 1/6 b) B=cfw_2,4,6 n(B) / n(S) = 3/6=1/2 c) C=cfw_3,4,5,6 n(C) / n(S) = 4/6=2/3 d) D=cfw_4,6 n(D) / (S)=2/6=1/3 (sixth) a) A=cfw_6 n(A) / n(S) = 1/6 b) B=cfw_1,3,5 n(B) / n

Penn State - STAT - 500

Stat 500 Homework 3 SolutionsSTAT500 HW#3 Solutions1) Random sample of 25 generated without replacement from Minitab (Will most likely differ from yours):2 240 125 409 783 526 219 364 584 789 84 341 296 652 134 708 104 155 21 562 378 522 86 667 4282)

Penn State - STAT - 500

STAT500 HW#4_solutionsSTAT500 HW#4 Solutions1) a) 95% T Confidence IntervalsVariable speed 10.304) N 20 Mean 9.100 StDev 2.573 SE Mean 0.575 95.0 % CI (7.896,b) The normal probability plot for reading speed suggests no reason to believe that the data

Penn State - STAT - 500

STAT500 HW#5_solutionsSTAT500 HW#5 Solutions1) Chicago Title Company problem T 0 = 0.831; because nT 0 = 2544*(0.831) = 2114.1 > 5, n*(1 - T 0) = 2544*(1 0.831) = 429.9 > 5, thus the one-proportion z-test can be used. Ho: = 0.831; Ha: 0.831 = 0.024; two

Penn State - STAT - 500

STAT500 HW#6_solutionsHomework 6 Solutions1. a. This poses an interesting question since we never discussed intuitive decisions prior to performing an analysis. So here is an intuitive thought process. Since one assumption is that the each population fo

Penn State - STAT - 500

Solution to Homework 1 The following data were collected for a class of 20 students on reading readiness stanines (X) at the end of kindergarten and reading achievement stanines (Y) at the end of first grade. You want to examine how well the readiness sco

Penn State - STAT - 500

Solution to Homework 1 The following data were collected for a class of 20 students on reading readiness stanines (X) at the end of kindergarten and reading achievement stanines (Y) at the end of first grade. You want to examine how well the readiness sco

Penn State - STAT - 200

Solutions Displaying Data2.3 Identify the variable type: a) quantitative b) categorical c) categorical d) quantitative 2.6 Discrete or continuous?: a) continuous b) discrete c) continuous d) discrete 2.8 Number of children:a) The variable, number of chi

Penn State - STAT - 200

Solutions Gathering Data 4.5 School testing for drugs : Although this study found similar levels of drug use in schools that used drug testing and schools that did not, lurking variables might have affected the results. For example, it is possible that sc

Penn State - STAT - 200

Solutions - Probability Distributions 6.3 Boston Red Sox hitting: a) The probabilities give a legitimate probability distribution because each one is between 0 and 1 and the sum of all of them is 1. b) = 0P(0) + 1P(1) + 2P(2) + 3P(3) + 4P(4) = 0(0.718) +

Penn State - STAT - 200

Solutions - Sampling Distributions 7.6 Exit poll and n: a) The interval of values within the sample proportion will almost certainly fall within three standard errors of the mean: 0.53 to 0.59. b) Based on the interval calculated in (a), it would be unusu

Penn State - STAT - 200

Solutions - Hypothesis Testing9.4 Iowa GPA: H 0 : = 2.80Ha :2.80In the above hypotheses, H 0 : is the notation for the null hypothesis, H a : is the notation for the alternative hypothesis, and is the parameter, the mean GPA of the population, about w

Penn State - STAT - 200

Solutions - Categorical Variables11.3 FBI statistics: a) These distributions refer to those of x at given categories of y. RACE OF VICTIM RACE OF MURDERER Blacks WhitesBlacks Whites91% 9%17% 83%b) x and y are dependent because the probability of a mu

Penn State - STAT - 200

Confidence Intervals Proportion and One Mean1 The term sampling frame refers to the group that actually had a chance to get into the sample. Ideally, this is the same as the population of interest, but sometimes it isnt. In the following situation, descr

Penn State - PSYCH - 412

Growth Spurt: Muscle Mass and Body Fat Rapid acceleration in height and weight; significant boost in muscle and body fat By the end of puberty, the muscle to fat ratio is: Boys = 3:1 Girls = 5:4 Boys gain muscle at a faster rate than girls Girls gain fat

Penn State - PSYCH - 412

Changes in Cognition Logical Thinking Transductive Thinking: connects two particular events into a cause-effect relationship simply because they occurred close in time Inductive Thinking: we make inferences about the world based on a limited set of experi

Penn State - PSYCH - 412

Brain Development neuron: single cell unit of the central nervous system nerve: single cell unit of the peripheral nervous system dendrites: top of the neuron; extensions, branches; gather incoming information to pass it along to be processed soma (or cel

Penn State - PSYCH - 412

Social Redefinition a period when the individual is being redefined by their society, from that of a child towards that of an adult (increased privileges and responsibilities) social redefinition tends to be more pronounced in traditional societies compar

Penn State - PSYCH - 412

The Generation Gap occurs when older and younger people fail to understand one another due to their different experiences, opinions, habits and overall behaviorParent-Adolescent Conflict G. Stanley Hall (1904) believed in storm and stress Anna Freud (194

Penn State - PSYCH - 412

Adolescents and their Peers high school students spend twice as much time with their peers as their parents for boys, time spent with family is replaced with time spent alone for girls, time spent with family is replaced with time with friendsOrigins of

Penn State - PSYCH - 238

What do we know when we know a person? What we know about someone depends on how well we know them. However, you can never truly know everything about someone even ones own spouse or child. We often develop first impressions about individuals based on the

Penn State - PSYCH - 238

1. Say that you want to create a self-judgment questionnaire to measure extroversion. You know from reading the Lesson Commentary that research by Dr. Johnson identified seven kinds of statements in self-judgment personality questionnaires. Which of the s