Statistics Questions

The maximum weights in kilograms for which one repetition of a half squat can be performed and the times in seconds to run a 10 meter sprint for 12 international soccer players are shown attached data table with a sample correlation coefficient r of 0 977 A 13th data point was added to the end of the data set for an international soccer player who can perform the half squat with maximum of 210 kilograms and can sprint 10 meters in 1 99 seconds Describe how this affects the correlation coefficient r Use technology Click the icon to view the data set The new correlation coefficient r Round to three decimal places as needed going from 0 977 to Data table Player 1 2 3 4 5 6 7 8 9 10 11 12 13 Maximum weight x Time y 1 79 1 78 2 04 1 43 175 175 150 205 150 190 180 155 190 180 160 165 210 2 05 1 61 1 71 1 89 1 61 1 64 1 99 1 88 1 99 X

The accompanying data are the number of wins and the earned run averages mean number of earned runs allowed per nine innings pitched for eight baseball pitchers in a recent season Find the equation of the regression line Then construct a scatter plot of the data and draw the regression line Then use the regression equation to predict the value of y for each of the given x values if meaningful If the x value is not meaningful to predict the value of y explain why not p x 5 wins b x 10 wins c x 19 wins d x 15 wins Click the icon to view the table of numbers of wins and earned run average Round to two decimal places as needed Wins and ERA Wins x 8415 20 17 RIES 16 14 12 11 9 Earned run average y 2 72 3 23 2 71 3 79 3 89 4 26 3 79 5 05 X

The table to the right shows the average price of a movie ticket in a certain theater for the years 2009 to 2013 Draw a line graph that makes the increase in the average price of a movie ticket for the years shown appear to be small and another that makes the increase in the average price of a movie ticket for the years shown appear to be large O A Choose the line graph that makes the increase in the average price of a movie ticket for the years shown appear to be large O C OD 8 60 A Price 7 657 2008 Year 2014 Q OB 16 00 A Price 07 Year 2009 2010 2011 2012 2013 2008 Year Price 7 79 7 83 8 23 8 46 8 49 2014 10 35 APrice 4 151 2008 Year 2014 APrice 9 50 6 25 2008 Year 2014

HW 9 1 Basic Principles of Hypothesis Testing Question 9 of 9 1 point Question Attempt 1 of 3 Type I error A company that manufactures steel wires guarantees that the mean breaking strength in kilonewtons of the wires is greater than 50 They measure the strengths for a sample of wires and test Ho 50 versus H 50 Part 1 of 3 If a Type I error is made what conclusion will be drawn regarding the mean breaking strength The conclusion will be that the mean breaking strength is greater than 50 Part 1 3 Part 2 of 3 If a Type II error is made what conclusion will be drawn regarding the mean breaking strength king strength is Choose one 50 X

Determine whether the alternate hypothesis is left tailed right tailed or two tailed Ho 50 H 50 The alternate hypothesis is Choose one

Question 8 of 9 1 point Question Attempt 2 9 Coffee The mean caffeine content per cup of regular coffee served at a certain coffee shop is supposed to be less than 100 milligrams A test is made of Ho 100 versus H 100 The null hypothesis is rejected State an appropriate conclusion There Choose one enough evidence to conclude that the mean amount spent is Choose one more than less than different than 100 milligrams

Question 9 of 9 1 point Question Attempt 1 of 3 Part 0 3 6 Part 1 of 3 8 Type I error A company that manufactures steel wires guarantees that the mean breaking strength in kilonewtons of the wires is greater than 50 They measure the strengths for a sample of wires and test Ho 50 versus H 50 If a Type 1 error is made what conclusion will be drawn regarding the mean breaking strength The conclusion will be that the mean breaking strength is Choose one 50 equal to not equal to less than 9 greater than lers than or greater than

2 3 4 6 The alternate hypothesis is Choose one left tailed right tailed two tailed 7 Determine whether the alternate hypothesis is left tailed right tailed or two tailed Ho u 19 H 19 8 9

5 The outcome of the test is a Choose one Type 1 error correct decision Type 11 error 6 Determine whether the outcome is a Type I error a Type 11 error or a correct decision A test is made of H 55 versus H 55 The true value of is 55 and H is rejected 8 9

te word or phrase to complete the sentence en it is true is called a Choose one 7 error 06 Type II Type I 28 error and failing to reject Ho wher

3 4 5 6 Select the appropriate word or phrase to complete the sentence 7 8 9 The Choose one hypothesis states that a parameter is equal to a certain value while the Choose one hypothesis states that the parameter differs from this value X 80 do

Question 10 of 10 1 point Question Attempt 2 of 3 How s the economy A pollster wants to construct a 90 confidence interval for the proportion of adults who believe that economic conditions are getting better Part 0 2 Part 1 of 2 a A poll taken in July 2010 estimates this proportion to be 0 29 Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 02 adults is needed to obtain a 90 confidence interval with a margin of error of 0 02 X Espa ol 8 ME B

Question 5 of 10 1 point Question Attempt 3 of 3 b Construct an 80 confidence interval for the proportion of smartphone owners aged 18 24 who have an Android phone Round the answers to at least three decimal places An 80 confidence interval for the proportion of smartphone owners aged 18 24 who have an Android phone is 0 390 p 0 472 Part 2 3 Part 3 of 3 c Assume that an advertisement claimed that 46 of smartphone owners aged 18 24 have an Android phone Does the confidence interval contradict this claim The confidence interval Choose one contradict the claim because 0 46 Choose one contained in the confidence interval does does not X 5 Ella E

Part 2 of 3 b Construct a 99 confidence interval for the proportion of those aged 65 and over who have sleep apnea Round the answer to at least three decimal places A 99 confidence interval for the proportion of those aged 65 and over who have sleep apnea is 0 196 p 0 304 Part 2 3 S Part 3 of 3 c In another study medical researchers concluded that more than 32 of elderly people have sleep apnea Based on the confidence interval does it appear that more than 32 of people aged 65 and over have sleep apnea Explain Since all of the values in the confidence interval are Choose one 0 32 then the confidence interval Choose one contradict the claim 8 E

How s the economy A pollster wants to construct a 99 9 confidence interval for the proportion of adults who believe that economic conditions are getting better Part 1 of 2 X a A poll taken in July 2010 estimates this proportion to be 0 28 Using this estimate what sample size is needed so that the confidence interval will have a margin of error of 0 05 A sample of 1224 adults is needed to obtain a 99 9 confidence interval with a margin of error of 0 05 Correct Answer 874 Part 1 2 Part 2 of 2 b Estimate the sample size needed if no estimate of p is available Espa ol E M cl

Sleep apnea Sleep apnea is a disorder in which there are pauses in breathing during sleep People with this condition must wake up frequently to breathe In a sample of 432 people aged 65 and over 108 of them had sleep apnea Part 1 of 3 a Find a point estimate for the population proportion of those aged 65 and over who have sleep apnea Round the answer to at least three decimal places 0 250 The point estimate for the proportion of those aged 65 and over who have sleep apnea is Part 1 3 Part 2 of 3 b Construct a 99 confidence interval for the proportion of those aged 65 and over who have sleep apnea Round the answer to at least three decimal places A 99 confidence interval for the proportion of those aged 65 and over who have sleep apnea is Espa o O

Two dice are thrown a What are the odds in favor of getting a score of 12 b What are the odds against getting a 12 c What is the probability of getting a 12 a The odds in favor of getting a 12 are to Simplify

Question 3 Since Hill Valley High School eliminated the use of bells between classes teachers have noticed that more students seem to be arriving to class a few minutes late One teacher decided to collect data to determine whether the students and teachers watches are displaying the correct time At exactly 12 00 noon the teacher asked 9 randomly selected students and 9 randomly selected teachers to record the times on their watches to the nearest half minute The ordered data showing minutes after 12 00 as positive values and minutes before 12 00 as negative values are shown in the table below Students 4 5 3 0 0 5 0 0 0 5 0 5 1 5 5 0 Teachers 2 0 1 5 1 5 1 0 1 0 0 5 0 0 0 5 a Construct parallel boxplots using these data b Based on the boxplots in part a which of the two groups students or teachers tend to have watch times that are closer to the true time Explain your choice c The teacher wants to know whether individual students watches tend to be set correctly She proposes to test H u 0 versus H 0 where u represents the mean amount by which all student watches differ from the correct time Is this an appropriate pair of hypothesis to test to answer the teacher s question Explain why or why not Do not carry out the test

Quantitative variables are numerical values for which arithmetic operations such as means make sense It is usually a measure of some sort Categorical variables simply count which of several categories a person or thing falls Question 1 Are the following categorical or quantitative a zip codes e subjects listed according f students listed by to gender b list of subject heights social security number c the ages of several subjects recent test scores d the times it takes to make a button hole g students listed by

The area under the standard normal curve is 1 The standard deviation of the standard normal curve is 1 The mean of the standard normal curve is 0 5 What is the rule that describes 1 2 and 3 standard deviations from the mean Question 2 There are 4 basic typ problems 5 Students at the fine arts academy view on average five movies per semester with a standard deviation of two movies a What proportion of the students view more than six movies per semester b What proportion of the students view between 3 and 8 movies per semester c What proportion of the students view less than two movies per semester d What number separates the bottom 15 from the rest

3 Independent Sample T Test A researcher is interested in the difference in rural and urban people s attitudes towards gun control The researcher measures 30 participant s attitudes using a scale where higher ratings represent greater support for gun control bills The researcher gathers 30 participants 15 rural and 15 urban to gather their ratings Use an a 17 0 01 Urban Rural 9 90 9 24 6 25 4 30 6 80 4 30 4 80 6 50 13 25 3 30 5 26 4 70 8 00 9 25 10 22 1 25 6 95 6 50 5 96 5 25 2 36 9 25 6 36 4 25

HW Problem 49 5 pts A manufacturing firm which produces specialty rods wants to pick the machine which produces them the most consistently i e with the least variability The owner is considering the purchase of a new machine However before he spends the money on the new machine he wants to be certain that the variability of the output on the new machine is any different than the variability of the output on his existing machine He randomly selects 20 specialty rods produced by his existing machine which yields a sample mean diameter of 9 millimeters with a sample standard deviation of 4 15 microns 22 rods produced by the new machine result in a sample mean diameter of 9 millimeters with a sample standard deviation of 2 1 microns At the 01 level of significance test to see if the variance of output is different for the two machines List and clearly label all eight steps

Given the 5 categories in the table below test the claim that the categories are equally likely to be selected at a a 0 01 significance level Ho all 5 categories are equally likely to be selected Ha at least one category is not equally likely to be selected Category A B C D E Observed Frequency 14 13 13 5 8 What are the degrees of freedom d f OF I What is the critical value for this sample Round to four decimal places Part 2

Out of a sample of 100 adults aged 18 to 30 34 still lived with their parents Based on this construct a 90 confidence interval for the true population proportion of adults ages 18 to 30 that still live with their parents Give your answers rounded to 4 decimal places Select an answer

Out of of a sample of 400 families 180 had children under the age of 18 living in the home Based on this construct a 95 confidence interval for the true population proportion of families with children under the age of 18 living in the home Give your answers rounded to 4 decimal places Select an answer

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car They randomly survey 414 drivers and find that 309 claim to always buckle up Construct a 90 confidence interval for the population proportion that claim to always buckle up Select an answer Do not round between steps Round answers to at least 4 decimal places

A study was conducted to determine whether there were significant differences between college students admitted through special programs such as retention incentive and guaranteed placement programs and college students admitted through the regular admissions criteria It was found that the graduation rate was 92 6 for the college students admitted through special programs If 12 of the students from the special programs are randomly selected find the probability that at least 11 of them graduated prob If 12 of the students from the special programs are randomly selected find the probability that eactly 9 of them graduated prob Would it be unusual to randomly select 12 students from the special programs and get exactly 9 that graduate O yes it is unusual O no it is not unusual If 12 of the students from the special programs are randomly selected find the probability that at most 9 of them graduated prob Would it be unusual to randomly select 12 students from the special programs and get at most 9 that graduate O no it is not unusual yes it is unusual Would it be unusual to randomly select 12 students from the special programs and get only 9 that graduate O yes it is unusual Ono it is not unusual

Out of 600 people sampled 66 preferred Candidate A Based on this estimate what proportion of the voting population p prefers Candidate A Use a 99 confidence level and give your answers as decimals to three places

A student was asked to find a 98 confidence interval for the proportion of students who take notes using data from a random sample of size n 80 Which of the following is a correct interpretation of the interval 0 12 p 0 27 Check all that are correct There is a 98 chance that the proportion of the population is between 0 12 and 0 27 There is a 98 chance that the proportion of notetakers in a sample of 80 students will be between 0 12 and 0 27 The proportion of all students who take notes is between 0 12 and 0 27 98 of the time With 98 confidence the proportion of all students who take notes is between 0 12 and 0 27 With 98 confidence a randomly selected student takes notes in a proportion of their classes that is between 0 12 and 0 27

Given the 4 categories and distribution apply the Goodness of fit test at a 0 025 for the claim that the 4 categories occur with the following distribution Category A gives 40 category B gives 30 category C gives 10 and category D gives 20 of the distribution Ho the categories correspond to the given distribution Ha at least one category does not correspond to the given distribution Complete the table by calculating the expected frequencies Category A B Observed Expected Frequency Frequency 32 23 Part 2 of 6

1 Single Sample T test A researcher would like to study the effect of alcohol on reaction time It is known that under regular circumstances the distribution of reaction times is normal with 200 A sample of 10 subjects is obtained Reaction time is measured for each individual after consumption of alcohol Their reaction times were 219 221 222 222 227 228 223 230 228 and 232 Use a 0 05

Biologists studying the healing of skin wounds measured the rate at which new cells closed a razor cut made in the skin of an anesthetized newt Here are the data from 11 newts measured in micrometers per hour 10 11 12 46 13 14 18 21 27 66 28 The right whisker of a horizontal modified boxplot of this data should extend to

Bob runs a huge chicken farm with thousands of chickens Weight of eggs is random and varies from chicken to chicken The distribution of weight of eggs is known to be normal with a standard deviation of 5 grams Let X represent weight of eggs and x the population average weight of eggs on Bob s farm Bob sells eggs to a wholesaler who requires the average weight of eggs to be 65 grams You are asked to verify if eggs from Bob s farm satisfy the requirements of the wholesaler You took a sample of 100 eggs and computed a sample average weight of 64 grams Write the null and alternative hypothesis use two sided alternative relevant for the current problem Write your answer in this box

You are performing a Chi Square test with test statistic x 1 33 and degrees of freedom of 12 find the p value to 4 decimal places P value is 4

Suppose that water usages in American showers are normally distributed with an average shower using 18 9 gallons and a standard deviation of 3 6 gallons Estimate the percentage of showers that used a between 15 3 and 22 5 gallons b more than 26 1 gallons c less than 8 1 gallons d between 8 1 and 26 1 gallons

You are performing a Chi Square test with a level of significance of a 0 93 and degrees of freedom of 13 find the critical value to 4 decimal places Critical value is

A population of values has a normal distribution with 218 7 and o 95 1 You intend to draw a random sample of size n 48 Find the probability that a single randomly selected value is greater than 236 5 P X 236 5 Find the probability that a sample of size n 48 is randomly selected with a mean greater than 236 5 P M 236 5 Enter your answers as numbers accurate to 4 decimal places Answers obtained using exact z scores or Z scores rounded to 3 decimal places are accepted

Suppose this distribution represents the probabilities of extending our class 2 minutes past the end of class time 0 20 0 1 5 The variable z is Select an answer because there exist fractional amounts of time 2 3 4 The total area of the distribution rectangle is distribution and the sum of all the probabilities should be 1 which makes sense as it is a probability The probability in decimal form of the class extending 3 or more minutes beyond the end time is found by determining the area to the right of a 3 or the complement of the area to the left The probability in decimal form of the class extending 3 or less minutes beyond the end time is found by determining the area to the left of 3 Remember that when we read our distribution tables for many of our distributions the area quoted in the tables is to the left so it is important to be able to recognize the need for using the complement to find

Select an answer Distributi Snapes Determine the shape of each distribution shown below n Select an answer Select an answer Select an answer

For a goodness of fit test for a distribution with 3 categories what are the degrees of freedom for the x distribution for this test degrees of freedom

On a particular college campus 30 of the students belong to a fraternity or sorority If 50 college students are randomly chosen a What is the probability that no more than 14 are members of a fraternity or sorority Round to at least three decimal places b What is the mean of this distribution Round to at least one decimal c What is the standard deviation of this distribution Round to at least one decimal

XOT23 P x 0 0 15 1 0 25 0 15 3 0 45 Find the standard deviation of this probability distribution Give your answer to at least 2 decimal pl

Biologists tagged 193 fish in a lake on January 1 On February 1 they returned and collected a random sample of 33 fish 11 of which had been previously tagged On the basis of this experiment approximately how many fish does the lake have

Suppose a vector x exists in your workspace Which of the following commands will always output a logical vector of the same length as x with all of its elements being FALSE For example if the length of x is 3 then the output of the command should be 1 FALSE FALSE FALSE rep FALSE x logical length x Ox FALSE O X X

Do shoppers at the mall spend the same amount of money on average the day after Thanksgiving compared to the day after Christmas The 56 randomly surveyed shoppers on the day after Thanksgiving spent an average of 149 Their standard deviation was 26 The 56 randomly surveyed shoppers on the day after Christmas spent an average of 140 Their standard deviation was 44 What can be concluded at the a 0 01 level of significance For this study we should use Select an answer a The null and alternative hypotheses would be Ho Select an answer Select an answer H Select an answer Select an answer Select an answer Select an answer b The test statistic c The p value d The p value is a e Based on this we should Select an answer the null hypothesis f Thus the final conclusion is that C please show your answer to 3 decimal places Please show your answer to 4 decimal places The results are statistically insignificant at a 0 01 so there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is a different amount of money compared to the population mean amount of money that day after Christmas shoppers spend The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is a different amount of money compared to the population mean amount of money that day after Christmas shoppers spend The results are statistically significant at a 0 01 so there is sufficient evidence to conclude that the mean expenditure for the 56 day after Thanksgiving shoppers that were observed is a different amount of money compared to the mean expenditure for the 56 day after Christmas shoppers that were observed The results are statistically insignificant at a 0 01 so there is statistically significant evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is equal to the population mean amount of money that day after Christmas shoppers spend

Which of the following functions is not a vectorized function O is finite O is infinite O is na

Suppose a logical vector x exists in your workspace Which of the following commands results in output identical to the output of all x O any x O any x O any x identical x TRUE

What is the output when you subset a numeric vector at an index greater than the length of the vector O NULL NaN

Is it possible to decrease the length of a vector using subsetting without redefining the entire object For example redefining the entire object in this case refers to assignment such as obj OTHER OBJECT O No

Listed below are heights of a random sample of men and women Men Women 186 7 166 8 176 7 176 7 174 2 176 4 171 4 174 8 175 0 178 7 161 2 167 6 166 0 153 2 160 6 178 1 169 2 135 0 163 4 171 3 a Construct a 96 confidence interval for the difference between the mean heights of men and women Critical value z or t Enter the positive one Margin of Error E Confidence Interval b Interpret your result in part a in a complete sentence c Based on your confidence interval can you conclude that the mean height of men differs from the mean height of women Yes No