Statistics Topics

Macy is studying graphs of functions y fx Each set in the table contair some points on a particular graph Decide whether each set of points MIGHT BE on the graph of a function o CANNOT BE on the graph of a function 3 3 0 0 3 3 6 6 9 9 3 0 0 0 3 0 0 6 9 0 0 3 0 0 0 3 0 6 0 9 Yes O O No O

who support stricter gun control laws has been 52 A recent Gallup Poll of 1011 people showed 495 in favor of stricter gun control laws Assume the poll was given to a random sample of people Test the claim that the proportion of those favoring stricter gun control has changed Perform a hypothesis test using a significance level of 0 05 See page 405 for guidance Choose one of the following conclusions i The percentage is not significantly different from 52 A significant difference is one for which the p value is less than or equal to 0 050 The percentage is significantly different from 52

7 3 x vs Two symbols are used for the mean and x a Which represents a parameter and which a statistic b In determining the mean age of all students at your school you survey 30 students and find the mean of their ages Is this mean x or

bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 0000 T T 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 A resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math class In the class are three juniors and two seniors Using numbers 1 2 and 3 to represent juniors and 4 and 5 to represent seniors sample with out replacement Draw a sample of two people four times once in each of parts a b c and d and then fill in the following table 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 31 Fair Coin One of the graphs shows the proportion of heads from flipping a fair coin 10 times repeatedly The others do not Which graph represents the coin flips Explain how you know SECTION EXERCISES CHAPTER7 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 Repetition 1 from part a 2 from part b 3 4 a Use the first line reprinted here from the random number table to select your sample of two The selections are underlined 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the number of 4 s and 5 s and divide by the sample size 2 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 07033 75250 34546 75298 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09541 09084 98948 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples p Population Proportion of Seniors 2 5 0 4 347 80623 p Sample Proportion of Seniors 1 2 0 5 Error p p 0 5 0 4 0 1 7 34 Simulation From a very large essentially infinite population of which half are men and half are women you take a random sample with replacement Use the following random number table and assume each single digit represents selection of one person the odd numbers represent women and the even numbers 0 2 4 6 8 men a Start on the left side of the top line with 118 and count 10 people What percentage of the sample will be men

a If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 B amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 A resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math class In the class are three juniors and two seniors Using numbers 1 2 and 3 to represent juniors and 4 and 5 to represent seniors sample with out replacement Draw a sample of two people four times once in each of parts a b c and d and then fill in the following table a Use the first line reprinted here from the random number table to select your sample of two The selections are underlined 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the number of 4 s and 5 s and divide by the sample size 2 b Use the next line to select your sample of two 31867 Report the percentage of seniors in the sample 85872 91430 45554 c Use the next line to select your sample of two 07033 75250 34546 75298 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09084 98948 09541 80623 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 31 Fair Coin One of the graphs shows the proportion of heads from flipping a fair coin 10 times repeatedly The others do not Which graph represents the coin flips Explain how you know SECTION EXERCISES CHAPTER 7 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 Repetition 1 from part a 2 from part b 3 4 p Population Proportion of Seniors 2 5 0 4 347 Sample Proportion of Seniors 1 2 0 5 Error p p 0 5 0 4 0 1 7 34 Simulation From a very large essentially infinite population of which half are men and half are women you take a random sample with replacement Use the following random number table and assume each single digit represents selection of one person the odd numbers represent women and the even numbers 0 2 4 6 8 men a Start on the left side of the top line with 118 and count 10 people What percentage of the sample will be men

8 2 Choose one of the answers in each case In statistical infer ence measurements are made on a sample or population and generalizations are made to a sample or population

on your jury CTION 7 2 Targets Bias or Lack of Precision If a rifleman s gunsight is adjusted incorrectly he might shoot bullets consistently close to 2 feet left of the bull s eye target Draw a sketch of the target with the bullet holes Does this show lack of precision or bias Draw a second sketch of the target if the shots are both unbiased and precise have little variation The rifleman s aim is not perfect so your sketches should show more than one bullet hole Targets Bias or Lack of Precision Again If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 HL 0000000 oooo amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math cla the class are three juniors and two seniors Using numbers 1 3 to represent juniors and 4 and 5 to represent seniors sampl out replacement Draw a sample of two people four times or each of parts a b c and d and then fill in the following tab a Use the first line reprinted here from the random number tabl select your sample of two The selections are underlined 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the num 4 s and 5 s and divide by the sample size 2 7 26 Random Letters Samuel Morse suggested in the nineteent century that the letter t made up 9 of the English language Assume this is still correct A random sample of 1000 letters is take from a randomly selected large book and the t s are counted a What value should we expect for our sample percentage of t s b Calculate the standard error c Use your answers to fill in the blanks We expect t s give or take 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 27 ESP A Zener deck of cards has cards that show one of five different shapes with equal representation so that the probability c selecting any particular shape is 0 20 A card is selected randomly and a person is asked to guess which card has been chosen The graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his c her proportion of successes should be about 0 20 give or take som SECTION EXERCISES CHAPTER 7 7 32 Far from Fair Which of the graphs in Exercise 7 31 centered farthest from 0 50 b Use the next line to select your sample of two 31867 91430 45554 85872 Report the percentage of seniors in the sample c Use the next line to select your sample of two 07033 75298 75250 34546 Report the percentage of seniors in the sample d Use the last line to select your sample of two 09084 80623 98948 09541 Report the percentage of seniors in the sample e Fill in the rest of the table below showing the results of the four samples p Population p Sample

8 1 Choose one of the answers given The null hypothesis is sample statistic or always a statement about a population parameter

7 60 Human Cloning In a Gallup Poll 441 of 507 adults said it was morally wrong to clone humans a What proportion of the respondents believed it morally wrong to clone humans b Find a 95 confidence interval for the population proportion who believed it is morally wrong to clone humans Assume that Gallup used a simple random sample c Find an 80 confidence interval using a z of 1 28 if you are calculat ing by hand d Which interval is wider and why

8 7 Heart Attack Prevention A new drug is being tested to see whether it can reduce the chance of heart attack in people who have previously had a heart attack The rate of heart attack in the popula tion of concern is 0 20 The null hypothesis is that p the population proportion using the new drug that have a heart attack is 0 2 Pick the correct alternative hypothesis i p 0 2 ii p 0 2 iii p 0 2

7 2 Sample vs Census Explain the difference between a sample and a census Every 10 years the U S Census Bureau takes a census What does that mean

7 5 Ages of Presidents Suppose you knew the age at inaugu ration of all the past U S presidents Could you use those data to make inferences about ages of past presidents Why or why not

8 8 Stroke Survival Rate The proportion of people who live after suffering a stroke is 0 85 Suppose there is a new treatment that is used to increase the survival rate Use the parameter p to represent the population proportion of people who survive after a stroke For a hypothesis test of the treatment s effectiveness researchers use a null hypothesis of p 0 85 Pick the correct alternative hypothesis i p 0 85 ii p 0 85 iii p 0 85

8 6 Water A friend is tested to see whether he can tell bottled water from tap water There are 30 trials half with bottled water and half with tap water and he gets 18 right a Pick the correct null hypothesis 0 50 ii p 0 60 i p iii p 0 50 b Pick the correct alternative hypothesis i p 0 50 ii p 0 875 iii p 0 50 iv p 0 60 iv p 0 875

a If a rifleman s gunsight is adjusted correctly but he has shaky arms the bullets might be scattered widely around the bull s eye target Draw a sketch of the target with the bullet holes Does this show variation lack of precision or bias Explain how you can tell from the widths of the graphs which has the largest sample n 40 and which has the smallest sample n 10 1 amount Each dot in the dotplots represents the proportion of suc cess for one person For instance the dot in Figure A farthest to the right represents a person with an 80 success rate One dotplot rep TRY 7 33 What Is the Proportion of Seniors Example 5 A resents an experiment in which each person had 10 trials another shows 20 trials and a third shows 40 trials population of college students is taking an advanced math class In the class are three juniors and two seniors Using numbers 1 2 and 3 to represent juniors and 4 and 5 to represent seniors sample with out replacement Draw a sample of two people four times once in each of parts a b c and d and then fill in the following table reprinted here from the random number table to select your sample of two The selections are underlined Use the 02779 72645 32699 86009 Report the percentage of seniors in the sample Count the number of 4 s and 5 s and divide by the sample size 2 C T 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 Sample Proportion 7 28 ESP Again In the graph for Exercise 7 27 explain how you can tell from the shape of the graphs which has the largest sample size and which has the smallest sample size 7 29 Standard Error Which of the dotplots given in Exercise 7 27 has the largest standard error and which has the smallest stan dard error 7 30 Bias Assuming that the true proportion of success for the trials shown in the graph for Exercise 7 27 is 0 2 explain whether any of the graphs shows bias graph below shows a computer simulation of experiments in which a person was asked to guess which card had been selected for a large number of trials If the person does not have ESP then his or her proportion of successes should be about 0 20 give or take some 7 31 Fair Coin One of the graphs shows the proportion of heads from flipping a fair coin 10 times repeatedly The others do not Which graph represents the coin flips Explain how you know SECTION EXERCISES 7 32 Far from Fair Which of the graphs in Exercise 7 31 is centered farthest from 0 50 CHAPTER 7 b Use the next line to select your sample of two 31867 85872 91430 45554 Report the percentage of seniors in the sample c Use the next line to select your sample of two 75250 34546 75298 Report the percentage of seniors in the sample 07033 d Use the last line to select your sample of two 98948 09541 80623 Report the percentage of seniors in the sample 09084 e Fill in the rest of the table below showing the results of the four samples Repetition 1 from part a 2 from part b 4 p Population Proportion of Seniors 2 5 0 4 347 p Sample Proportion of Seniors 1 2 0 5 Error pp 0 5 0 4 0 1 7 34 Simulation From a very large essentially infinite population of which half are men and half are women you take a random sample with replacement Use the following random number table and assume each single digit represents selection of one person the odd numbers represent women and the even numbers 0 2 4 6 8 men a Start on the left side of the top line with 118 and count 10 people What percentage of the sample will be men

8 5 Magic A magician claims he can cause a coin to come up heads more than 50 of the time A coin is flipped 40 times and 35 heads come up a Pick the correct null hypothesis i P 0 50 ii p 0 875 b Pick the correct alternative hypothesis i p 0 50 iii p 0 50 ii p 0 875 iii p 0 50 iv p 0 875 iv p 0 875