Introductory Statistics Lectures Quizzes Anthony Tanbakuchi Department of Mathematics Pima Community College Compile date Tue Apr 14 09 06 16 2009 Contents 1 Quizzes 1 1 Intro material Basic Defs Descriptive Statistics 1 2 Probability 1 3 Random Variables Binomial Distribution Normal Distribution Central Limit Theorem 1 4 Hypothesis Testing 1 1 1 1 2 2 3 3 3 3 4 1 5 1 6 Basics Contingency Tables Independence Homogeneity Regression ANOVA Linear Correlation Admin Student Evaluations Exam Seating 4 4 4 4 5 5 6 Quizzes 1 1 Intro material BASIC DEFS Quiz Questions 1 A researcher discovered a data entry error that caused her estimate of the mean amount of carbon dioxide in the atmosphere to be too low Would this error be classified as a sampling error or a non sampling error 2 Which type of sampling would be likely to introduce less bias a random sample or a simple random sample 3 What would you type to store the data set 3 4 2 8 in the variable x using R 4 To estimate the mean height of students at Pima CC we randomly select 5 classrooms and measure the height of all of the students in the 5 selected rooms What type of sampling was used simple random sample convenience sampling systematic sampling stratified sampling or cluster sampling 5 What level of measurement does time in years represent nominal ordinal interval or ratio 1 2 of 7 1 2 Probability DESCRIPTIVE STATISTICS Quiz Questions 1 In a histogram what do the heights of the bars represent 2 Is a Parato chart used for qualitative or quantitative data 3 Let x 1 2 3 4 Fully simplify the following expression X xi 2 4 Let z 4 0 3 Fully simplify the following expression qX zi2 5 BONUS Using only the variable i write the following expression in summation notation 2 4 6 8 10 Quiz Questions 1 What does the standard deviation represent in words be specific 2 What percentage of data would fall within 3 as stated by the Empirical Rule 3 If we classify a data point as unusual what must its z score s magnitude absolute value be greater than 4 Which measure of center is least resistant most affected by outliers the mean median or mode 5 On a statistics exam Q1 72 and Q3 94 What percent of students had a score that fell within the IQR 1 2 Probability Quiz Questions 1 On a statistics exam Q1 72 and Q3 94 What percent of students had a score that fell within the IQR 2 An event A is defined as unusual if P A x What is the value of x Use the table below for the following questions The table lists the color red blue 8 2 and size of marbles in a bag small large 4 6 3 What is the probability of randomly selecting a red marble 4 What is the probability of randomly selecting a red marble or a small marble 5 Find the probability of the compliment for the previous question Anthony Tanbakuchi MAT167 Quizzes 3 of 7 Quiz Questions 1 If a couple plans to have 3 children what is the probability that they will have at least one girl 2 What is the probability that two randomly selected people were born on the same day of the year 3 What is the probability twins have the same birthday Think simple 4 If a class has 10 males and 10 females what is the probability of randomly selecting 2 females without replacement 1 3 Random Variables BINOMIAL DISTRIBUTION Quiz Questions A statistics class consists of 100 students and 85 are right handed Answer the following questions if 4 students are randomly selected without replacement 1 Can the binomial distribution be used for this question Yes No 2 If we are interested in finding the probability that 3 in 4 students are left handed what are x n and p for this problem 3 Find the probability that 3 in 4 students are left handed 4 Find the probability that 2 or fewer students in 4 are left handed NORMAL DISTRIBUTION Quiz Questions Assume that heights of women are normally distributed with 63 6 in and 2 5 in 1 A women s club for tall people has a membership requirement that women must be at least 70 in tall What percentage of women meet this requirement Make a sketch and do the calculation 2 The club s membership is too low they want to reduce the requirement so that the tallest 25 of women will be able to enter the club What should the new height requirement be Make a sketch and do the calculation CENTRAL LIMIT THEOREM Quiz Questions The following questions regard x and the Central Limit Theorem 1 What is the difference between a population distribution and a sampling distribution Anthony Tanbakuchi MAT167 4 of 7 1 4 Hypothesis Testing 2 To satisfy the Central Limit Theorem one of two requirements must be met What are the two requirements 3 If we satisfy the CLT requirements what type of distribution will x s have 4 BONUS What is the equation for x 1 4 Hypothesis Testing BASICS Quiz Questions Answer the following basic questions on hypothesis testing 1 A global warming researcher believes that the mean daily maximum temperature has increased from 82 2 degrees What is the null hypothesis H0 Hint H0 2 What is the alternative hypothesis Ha 3 In hypothesis testing we calculate the probability of observing the sample data p value assuming one of the hypotheses is true Do we assume the null hypothesis H0 is true or the alternative hypothesis Ha is true 4 What is the decision rule we use to reject the null hypothesis H0 5 When does a Type I error occur CONTINGENCY TABLES INDEPENDENCE HOMOGENEITY Quiz Question Each respondent in the Current Population Survey of March 1993 was classified as employed unemployed or outside the labor force The results for men in California age 35 44 can be cross tabulated by marital status as follows Married Divorced Never Married Employed 679 103 114 Unemployed 63 10 20 18 25 Not in labor force 42 1 What are the two variables in this contingency table 2 What is H0 and Ha 3 If the p value 0 and 0 05 what would your formal decision be 4 What is your conclusion 1 5 Regression ANOVA LINEAR CORRELATION Quiz Questions Anthony Tanbakuchi MAT167 Quizzes 5 of 7 2 0 8 6 4 2 y 1 2 3 4 x Use the above plot to answer the following questions Assume the relationship is significant 1 Classify the relationship as either perfect positive linear correlation positive perfect negative negative or non linear correlation 2 Which linear correlation coefficient best matches the data 5 1 0 8 0 08 0 0 08 0 8 1 5 3 Based on your above answer what percent of variation in y is explained by x 1 6 Admin STUDENT EVALUATIONS Student Evaluations Information Instructor Tanbakuchi Course MAT167 Section 22684 Campus West Class Time TR 9 10