Statistics Questions and Answers

Sam counts how many people came to the local political meeting He counts 72 people but forgot about the 4 people sitting behind him The percent error in his calculation is O 5 3 O 5 6 O O 2 8 50

Rachel recorded the number of calls she made at work during the week Day Monday Tuesday Wednesday Thursday x 0 E E O 3 27 Calls O 1 52 18 She expected to make 18 calls each day To answer whether the number of calls follows a uniform distribution a chi square test for goodness of fit should be performed alpha 0 10 O 3 11 14 24 What is the chi squared test statistic Answers are rounded to the nearest hundredth 16

A fast food restaurant gave a Customer Satisfaction Survey in which 1500 customers rated how satisfied they were with service The results are shown below as a table Extremely Satisfied Satisfied Neutral Dissatisfied Extremely Dissatisfied O 24 9 O 29 5 O 20 3 Rating O 38 5 234 443 246 The relative frequency of people who were extremely dissatisfied with the service is 203 374 Frequency

stion 2 he value of to such that the following

Find the value of to such that the following statement is true P to t to 0 99 where df 9 O 2 262 2 282 O 1 761 1 833

Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country The plot shows a strong positive correlation Brad recalls that correlation does not imply causation In this example Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance O Average annual salary per household O Average health insurance costs in the United States O The number of different car brands O The number of citizens in the United States who do not have health insurance

This scatterplot shows the performance of a thermocouple using the variables temperature difference and voltage Voltage in mV LO 5 4 5 4 3 5 3 2 5 2 1 5 5 0 Performance of a Thermocouple 10 30 40 50 60 Temperature Difference in C 20 Select the answer choice that accurately describes the data s form direction and strength in the scatterplot Form The data pattern is nonlinear O Direction There is a positive association between temperature difference and voltage Strength The data pattern is weak Form The data pattern is linear O Direction There is a negative association between temperature difference and voltage Strength The data pattern is strong Form The data pattern is linear O Direction There is a positive association between temperature difference and voltage Strength The data pattern is strong 70 80

his scatterplot shows the maintenance expense for a truck based on its years of service Maintenance Expense in dollars 600 500 400 300 200 Maintenance Expense Vs Age of Truck 100 O 703 O 549 O 2 The equation for least regression line to this data set is 76 82x 88 56 What is the predicted value in dollars for maintenance expenses when a truck is 7 years old 4 6 8 Age of Truck in years 10 12

Which of the following statements is TRUE O A high correlation is insufficient to establish causation on its own O If the two variables of a scatterplot are strongly related this condition implies causation between the two variables O A correlation of 1 or 1 implies causation O Only a correlation equal to 0 implies causation

The scores of the quizzes of five students in both English and Science are Student 1 O 0 42 Student 2 O 0 05 Student 3 O 0 23 Student 4 Student 5 y r 1 X X 7 Sx Sy English 6 LO 5 For English the mean is 6 4 and the standard deviation is 2 0 For Science the mean is 7 and the standard deviation is 1 6 9 4 8 Science 00 8 5 Using the formula below or Excel find the correlation coefficient r for this set of scores Answer choices are rounded to the nearest hundredth 69 7 9

A scientist is comparing parts of the body The tibia length is plotted against the body length as shown below Tibia Length Compared to Body Length 72 70 0000 68 66 Body Length inches 23 64 60 58 11 inches O 14 inches Using the best fit line approximately how long would the tibia bone be if the body length is 62 inches 6 12 inches 8 10 12 14 Tibia Length inches 16 18

Which statement about correlation is FALSE O A correlation of 1 or 1 corresponds to a perfectly linear relationship O Correlation is measured by r the correlation coefficient which has a value between 1 and 1 O Correlation is a quantitative measure of the strength of a non linear association between two variables O Correlation is a quantitative measure of the strength of a linear association between two variables

The scatterplot below charts the performance of an electric motor Speed of Rotation in RPMs O 3000 O 2800 O 2700 2600 2500 2400 2300 2200 2100 2000 Performance of an Electric Motor 1350 Explanatory variable Voltage Response variable Rotation Explanatory variable Voltage Response variable Electric motor 1400 Which answer choice correctly indicates the explanatory variable and the response variable of the scatterplot Explanatory variable Rotation Response variable Electric motor 1450 1500 1550 Voltage in mVs 1600 1650 1700 1750

For the plot below the value of r is 0 7783 Cost in dollars 700 525 350 175 O O Cost of Airplane Ticket vs Miles Flown 750 Which of the following sets of statements is true 1500 Distance from MSP in miles About 78 of the variation in ticket price can be explained by the distance flown The correlation coefficient r is 0 882 About 78 of the variation in distance flown can be explained by the ticket price The correlation coefficient r is 0 606 About 88 of the variation in ticket price can be explained by the distance flown The correlation coefficient r is 0 882 2250 About 22 of the variation in ticket price can be explained by the distance flown 3000

Shawna finds a study of American women that has an equation to predict weight in pounds from height in inches y 260 6 6x Shawna s mom s height is 68 inches and her weight is 179 pounds What is the residual of weight and height for Shawna s mom O 921 4 pounds O 188 8 pounds O O 9 8 pounds 9 8 pounds

Two cards are selected from a standard deck of 52 playing cards The first card is not replaced before the second card is selected Find the probability of selecting a black card and then selecting a red card

Question Completion Status 1 2 3 40 5 QUESTION 19 George Wallace is inter problems they have in He recruits a sample a Money 745 294 858 Problems 103 49 10 Match each statistic v

You randomly select an integer from 0 to 7 inclusively and then randomly select an integer from 0 to 4 inclusively What is the probability of selecting a 3 both times

uestion 1 of 8 Step 1 of 2 onsider the value of t such that 0 01 of the area under the curve is to the right of t ep 1 of 2 Select the graph which best represents the given description of t swer 10 Points A A t t

Question 10 The foreign ownership of the U S government securities amounts to O 60 O 75 O 40 Points 2 O 10

A NASDAQ C FTSE International O A and C After the terrorist attack in New York on September 11 2001 which of the following stock exchanges experienced a downturn O A and D O A C and D B Nagoya A B C and D D CHX

QUESTION 15 Given X 100 94 77 99 71 83 and Y 45 36 20 44 17 24 24 Calculate The correlation coeffici Remember to report yo

on Completion Status 3 JESTION 9

Lab 3 Problem Set Name Temp X 57 77 Ice Cream Sales 215 401

files Tab Window Help New Ta XV CUNY X ke launch jsp course assessment id US Bb Take To 50 61 70 80 9 100 11

ESTION 1 earcher performing an obs ber of hours they spend pe

QUESTION 12 Given X 100 86 78 83 70 81 87 97

QUESTION 10 If a relationship is linear the relation can be most accurately re all the points fall on a curved line the relationship is best represented b all the points must fall on a straight lin

a must be positive a must be negative QUESTION 8 Which Pearson correlation coefficient shows 0 80 O 0 00 O 0 75 O 0 20 0 03 QUESTION 9 Which of the following statements concern Or 0 00 represents the absence of a r The relationship between the two varia

Which plan has the least amount of risk

In the long run which plan has the higher payout

In a recent poll 390 people were asked if they liked dogs and 80 said they did Find the margin of error of this poll at the 95 confidence level Give your answer to three decimals

Fall 2 1 A plastic bottle company is measuring the variation of the cap size that their newest machine produces They gather the data from 1500 bottle caps and calculate the mean and standard deviation The mean diameter of the bottle caps is 25 mm with a standard deviation of 1 mm Draw a Normal Distribution curve for this situation 1 point For each question show your work a Of the 1500 bottle caps measured how many bottle caps measured between 24 and 26 mm 1 point b Of the 1500 bottle caps measured how many bottle caps measured 25 mm or less 1 point c Of the 1500 bottle caps measured how many bottle caps measured between 22 and 28 mm 1 point d If you randomly choose 1 bottle cap and measure it what is the likelihood that it will be between 23 and 27 mm 1 point 2223 24 25 26 27 28

If n 560 and p p hat 0 4 find the margin of error at a 90 confidence level Round to 4 places

6 18 Is college worth it Part II Exercise 6 16 presents the results of a poll where 48 of 331 Americans who decide to not go to college do so because they cannot afford it a Calculate a 90 confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it and interpret the interval in context lower bound please round to four decimal places please round to four decimal places Interpret the confidence upper bound interval in context 90 of Americans choose not to go to college because they cannot afford it We can be 90 confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it We can be 90 confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval b Suppose we wanted the margin of error for the 90 confidence level to be about 1 5 How large of a survey would you recommend A survey should include at least people

e Jophia U Teri 28 pts 4 each Arrival times in minutes of donor organs in the population of US operating rooms can be modeled as a normal random variable X The mean arrival time is 40 min The standard deviation is 5 minutes a What is the R code needed to find number of minutes which corresponds to the 90th percentile aka 90th quantile of arrival times Norm b Sketch an area corresponding to P X 30 c Would an arrival time of 58 minutes be considered an outlier Why or why not d What Z score corresponds to an arrival time of 58 e The arrival time of 58 is how many standard deviations above the mean arriva f AZ score of 2 corresponds to what arrival time

Out of 600 people sampled 372 had kids Assuming the conditions are met construct a 99 confidence interval for the true population proportion of people with kids Give your answers as decimals to three places

Find the probability P 1 66 Z 1 66 Multiple Choice 0 050 0 904 0 929 J

For the next question use the following table of critical values of Z Confidence Level C 90 1 645 Critical Z Z b 4 What is the margin of error M 95 1 96 5 24 pts The systolic blood pressure for the population of US adults is known to be normally distributed with unknown mean and known standard deviation of 12 mmHg You are asked to construct a 90 confidence interval for the population mean systolic blood pressure for US adults You sample 36 US adults and find the sample mean is 120 mmHg a 4 What critical value of Z should you use 4 What is the confidence interval d 4 Write a sentence interpreting the confidence interval 99 2 576 Escore e 4 If you kept c 90 but increased the sample size would the width of your confidence interval increase decrease or remain the same WHY f 4 If you kept n 36 but increased your level of confide width of your confiden 22

4 24 pts 4 each The hourly wage for the national population of health aides denoted by X is known be normally distributed and to have a mean of 30 00 and a standard deviation of 6 00 A statistician plans to take a random sample of 16 health aides at some point in the future in an effort to study these salaries a Why can you assume the probability curve of Xbar is Normal b What are the mean and standard deviation of Xbar c If you took a larger sample would the standard deviation of Xbar increase decrease or remain the same d Compute the Zscore corresponding to a sample mean of 25 50 e What is the R code needed to compute the probability that the sample mean is less than 25 50 using the Zscore you computed Rcode PNorm f If you took a sample of health aides that was larger than 16 would the probability that the sample mean is less than 25 50 remain the same increase or decrease WHY No calculations needed

3 8 pts A medical screening test to detect a disease has the results summarized in the table below in millions of people Test Pos 12 57 69 a 4 pts Find the Sensitivity for this test Have Disease Yes No Total Result Neg 3 228 231 Total 15 285 300 b 4 pts Find the Positive Predictive Value PPV for this test

2 For problem 3 10 pts 5 each consider the table below of selected students from MA 151 last year You do NOT need to convert this table to percents avert this ta Yr MU 1 2 3 4 Total Bio 30 20 18 12 80 Major Health Studies Total 25 15 12 8 60 55 35 20 20 140 a If one student is chosen at random find the probability they are both a Bio major AND a 1st year b If one student is chosen at random from this group find the probability that they are a 1st year student OR a Bio major show your work

A table represents the number of students who passed or failed an aptitude test at two different campuses Passed Failed O 39 students O 50 5 students East Campus O48 3 students 39 O 42 students 61 In order to determine if there is a significant difference between campuses and pass rate the chi square test for association and independence should be performed West Campus What is the expected frequency of East Campus and passed 45 55

Which of the following assumptions for a two way ANOVA is FALSE O The groups must have the same sample size O The variances of the populations must be equal The sample populations must be normally or approximately normally distributed O The samples must be dependent

Emile has calculated a one tailed z statistic of 1 97 and wants to see if it is significant at the 5 significance level What is the critical value for the 5 significance level Answer choices are rounded to the hundredths place O 1 64 O 0

Adam tabulated the values for the average speed on each day of his road trip as 60 5 63 2 54 7 51 6 72 3 70 7 67 2 and 65 4 mph If Adam wanted to construct a one sample t statistic what would the value for the degrees of freedom be O 8 O 9 07 4

Carl recorded the number of customers who visited his new store during the week Day Monday Tuesday Wednesday Thursday x O 0 40 O 2 33 He expected to have 15 customers each day To answer whether the number of customers follows a uniform distribution a chi square test for goodness of fit should be performed alpha 0 10 0 E E O 1 60 Customers 17 O 0 67 13 What is the chi squared test statistic Answers are rounded to the nearest hundredth 14 16

What do the symbols x and s represent O Sample statistics O Population parameters O Defined variables O Variables of interest

Which of the following is an example of a parameter O All of the members of the community watch group gave their availability to volunteer over the summer Half of the receipts at the coffee shop include web address for giving feedback O 3 5 of the restaurant goers are given a survey to fill out O 9047 out of 531 310 citizens voted in the special election for city council

For the data plotted in the scatterplot the value was calculated to be 0 9846 Yearly income in thousand dollars 84 84 84 O 80 75 70 65 60 55 50 45 35 30 25 20 15 O Yearly Income vs Age 15 20 25 30 35 40 45 50 55 60 65 70 Age Which of the following sets of statements is true 98 5 of the variation in yearly income is explained by a nonlinear relationship with age The correlation coefficient r is 0 992 98 5 of the variation in yearly income is explained by a linear relationship with age The correlation coefficient r is 0 992 O 98 5 of the variation in age is explained by a nonlinear relationship with yearly income The correlation coefficient r is 0 969