Statistics Questions

Calculate the standard score of the given X value X 81 8 where 84 3 and o 82 3 Round your answer to two decimal places Answer to Fi

5 A production process for filling orange juice containers labeled as 64 ounces is monitored or the actual amount of juice in the container The process is designed such that the amount juice in the containers has a normal distribution with a mean of 64 3 ounces and a standard eviation of 15 ounces The process is monitored by randomly selecting 24 containers every our and measuring the actual amount of juice in the containers An increase in the standard 37 54 deviation beyond 15 ounces with the mean remaining at 64 3 ounces will result in a production run with too many underfilled and overfilled containers The following data are the actual amounts of juice in a random sample of 24 containers 64 26 64 22 64 42 64 13 64 44 64 64 64 19 64 12 63 98 64 34 64 20 64 31 64 15 64 09 63 85 64 17 64 21 64 23 64 33 64 19 64 57 64 19 a If the amount of juice in the containers has a normal distribution with a mean of 64 3 ounces and a standard deviation of 15 ounces what proportion of containers filled on the production line will be underfilled contain less than 64 ounces What percentage will be overfilled b Construct a 95 confidence interval on the process standard deviation c Do the data indicate that the process standard deviation is greater than 15 ounces Use a 05 in reaching your conclusion d What is the p value of your test e Is there any indication that the necessary conditions for constructing the confidence interval and conducting the test may be violated f What is the population about which inferences can be made using the given data

this company Race Coordinator 32 35 32 10 White Black Hispanic Asian Multiple Choice Seniority O Analyst 20 10 15 11 Manager 25 25 13 10 For the chi square test of independence to be valid Martha combines the seniorities Manager and Director Using the p value approach and a 0 05 the decision and conclusion are Director 9 5 2 0 do not reject the null hypothesis conclude race and seniority are independent do not reject the null hypothesis cannot conclude race and seniority are dependent reject the null hypothesis conclude race and seniority are independent

O In the following table likely voters preferences of two candidates are cross classified by gender Candidate A Candidate B Multiple Choice For the chi square test of independence the value of the test statistic is 4 2 34 3 25 Male 150 100 1 62 Female 130 120

The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007 Class in percent Observed Frequency Return 5 5 Return 0 0 Return 5 Return 25 Over the time period the following summary statistics are provided Mean 0 31 Standard deviation 6 49 Skewness 0 15 and Kurtosis 0 38 The probability that the return is less than 5 if the return is normally distributed is Multiple Choice 0 2358 0 2841 13 16 20 11 0 2061

1 Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range The following contingency table presents these results Class Income 50 000 50 000 Income 100 000 100 000 Income 150 000 Income 150 000 The test statistic for this sample is Multiple Choice 25 560 21 829 Less than 650 26 30 48 25 Credit Score 650 750 34 58 22 34 More than 750 21 46 35 21

5 The heights in cm for a random sample of 60 males were measured The sample mean is 166 55 the standard deviation is 12 57 the sample kurtosis is 0 12 and the sample skewness is 0 23 The following table shows the heights subdivided into non overlapping intervals Class Height 150 150 Height 160 160 Height 170 170 Height 180 Height 2 180 Multiple Choice O Observed 10 6 18 17 9 Suppose the value of the test statistic is 7 71 Using the critical value approach decision and conclusion are Expected pi 0 09 0 21 0 31 0 25 0 14 do not reject the null hypothesis conclude that heights are not normally distributed reject the null hypothesis conclude that heights are normally distributed reject the null hypothesis conclude that heights are not normally distributed do not reject the null hypothesis conclude that heights are normally distributed

A card dealing machine deals spades 1 hearts 2 clubs 3 and diamonds 4 at random as if from an infinite deck In a randomness check 1 600 cards were dealt and counted The results are shown below Suit Spades Hearts Clubs Diamonds Observed 410 405 370 415 Using the critical value approach the decision and conclusion are Multiple Choice reject the null hypothesis conclude that not all proportions are equal to 0 20 do not reject the null hypothesis we cannot conclude that not all of the proportions are equal to 0 25 do not reject the null hypothesis all of the population proportions are the same reject the pull hypothesis conclude that not all proportions are equal to 0 25

You are interested in finding a 90 confidence interval for the average number of days of class that college students miss each year The data below show the number of missed days for 13 randomly selected college students Round answers to 3 decimal places where possible 12 9 3 6 8 12 12 11 3 11 2 6 10 a To compute the confidence interval use a distribution b With 90 confidence the population mean number of days of class that college students miss is between and days c If many groups of 13 randomly selected non residential college students are surveyed then a different confidence interval would be produced from each group About 90 percent of these confidence intervals will contain the true population mean number of missed class days and about 10 percent will not contain the true population mean number of missed class days

Suppose a life insurance company sells a 300 000 1 year term life insurance policy to a 20 year old female for 280 According to the National Vital Statistics Report 58 21 the probability that the female survives the year is 0 999544 Compute and interpret the expected value of this policy to the insurance company The expected value is

The following table shows the distribution of employees in an organization Martha Foreman an analyst wants to see if race has a bearing on the position a person holds with this company Race White Black Director 9 5 2 Hispanic Asian 0 To test that race and seniority are independent the null and alternative hypothesis are Multiple Choice O Seniority O Coordinator Analyst 32 20 35 10 32 15 10 11 Manager 25 25 13 10 Ho Race and seniority are dependent HA Race and seniority are independent Ho Race and seniority are independent HA Race and seniority are dependent Ho Race and seniority are not mutually exclusive HA Race and seniority are mutually exclusive

A random sample of 20 adults in a particular country were asked to state what type of they use The results are in the table below None None None Condom Condom Condom Condom Condom Other None None Other None Condom Other None Pill Other Condom a Since data were collected for Select an answer variable s the correct graph to make is a Select an answer b Complete the frequency relative frequency table Birth Control Type None Pill None None Frequency Other c Which of the following is the correct bar chart for the given data Relative Frequency

You are interested in finding a 90 confidence interval for the average number of days of class that college students miss each year The data below show the number of missed days for 13 randomly selected college students Round answers to 3 decimal places where possible 12 9 3 6 8 12 12 11 3 11 2 6 10 a To compute the confidence interval use at distribution b With 90 confidence the population mean number of days of class that college students miss is between and days

Engin 7 15 A soft drink firm is evaluating an investment in a new type of canning machine The company has already determined that it will be able to fill more cans per day for the same cost if the new ma chines are installed However it must determine the variability of fills using the new machines and wants the variability from the new machines to be equal to or smaller than that currently obtained using the old machines A study is designed in which random samples of 40 cans are selected from the output of both types of machines and the amount of fill in ounces is determined The data are given below Old Machine New Machine 16 19 16 54 15 92 16 29 16 44 16 29 15 64 15 81 16 20 16 36 16 36 16 05 16 07 16 04 16 56 16 42 16 08 16 47 16 02 16 74 16 08 16 31 16 50 16 14 16 12 16 30 16 41 16 11 16 06 16 64 16 40 16 40 16 28 16 66 16 20 16 29 15 75 16 22 16 12 16 23 16 19 16 59 16 36 16 27 16 43 16 26 16 31 16 59 16 08 16 07 16 15 16 50 16 25 16 25 16 19 16 13 16 15 16 17 16 32 16 81 16 27 17 09 15 96 16 02 16 29 15 99 15 99 16 42 16 15 16 23

Find the 5 number summary for the data shown 6 24 29 75 90 96 5 number summary 6 25 5 60 IQR 11 27 45 78 91 97 90 5 97 The 1 5XIQR rule states that values between and are likely

On a recent exam a group of students had a mean score of 62 and a standard deviation of 7 If Chris achieved a score of 42 4 what would be the corresponding z score Answer The z score

The table below shows the gender distribution of students responding to the survey Use the table below to answer the following Over 3 0 2 0 3 0 Under 2 0 117 85 136 102 253 187 If one student is chosen at random what is Male Female Total The probability they are Female AND got Over a 3 0 use 4 decimals The probability they are Male OR got Under 2 0 use 4 decimals 38 36 74 Total 240 274 514

Assume that a sample is used to estimate a population mean Find the 99 confidence interval for a sample of size 1103 with a mean of 77 8 and a standard deviation of 17 2 Enter your answer as a tri linear inequality accurate to 3 decimal places AFA

Suppose you take a standardized test and you are in the 14 th percentile What does this percentile mean O 14 of the scores were higher than your score O you scored 14 lower than the class average O you scored 14 higher than the class average 14 of the scores were your score or lower Can you say that you failed the test O Yes since 14 is below 60 O It depends on how the rest of the class scored If scores were really high it is possible that I got a passing score O No since you scored 14 above the class average Olt depends on how the rest of the class scored If scores were really low on this exam it is possible that I got a passing score O No since 14 is below 60

An insurance company wants to estimate the percentage of 16 year olds who make an insurance claim in their first year of driving They take a sample of 1500 16 year olds who are insured with their company Match the following percentage of all 16 year olds who are insured with the company who make an insurance claim in their first year of driving 1500 16 year olds who are insured with the company 000 a 16 year old who is insured with the company whether or not they made an insurance claim in their first year of driving all 16 year olds who are insured with the company percentage of 1500 16 year olds who are insured with the company who make an insurance claim in their first year of driving a sample b parameter c variable d individual e statistic f population

The histogram below shows the age distribution of students responding to the survey Use this histogram to answer the following Note n 514 Frequency 400 350 300 250 200 150 100 50 0 10 Age Frequency Distribution 389 20 63 27 23 36 40 Ages Lower Class Limits 56 12 8 What is the frequency of the 26 35 age group How many students were under the age of 46 What is the shape of the distribution of the Age data Skewed left O Uniform O Skewed right O Bell shaped

The boxplot below shows pulse rates for a random sample of female subjects before and after one minute of exercise Before exercise HOH After exercise Before exercise Which pulse rates are more consistent overall O After exercise t 40 60 100 120 140 160 80 Pulse Rate of Female Subjects in beats per minute Which pulse rates are more consistent in the middle 50 O After exercise O Before exercise H The middle pulse rate is higher for which group O After exercise O Before exercise 180

Determine the shape of the distribution pictured below and the measure of center that should be used 30 Frequency s89858 25 20 15 10 0 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 data O Uniform O Bell shaped Skewed right Skewed left Based on the shape of the histogram above what measure of center should be used O mean median

Match the name of the sampling method descriptions given dividing by population by voting precinct and sampling everyone in the precints selected choosing every 5th person on a list ask all the students in your math class writing everyones name on a playing card shuffling the deck then choosing the top 20 dividing the population by Gender and choosing 30 people of each gender cards Sampling Method Situations a Convenience b Cluster c Systematic d Simple Random e Stratified

A fitness center is interested in finding a 90 confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center Records of 227 members were looked at and their mean number of visits per week was 3 2 and the standard deviation was 1 9 Round answers to 3 decimal places where possible a To compute the confidence interval use at distribution b With 90 confidence the population mean number of visits per week is between and visits c If many groups of 227 randomly selected members are studied then a different confidence interval would be produced from each group About 90 percent of these confidence intervals will contain the true population mean number of visits per week and about 10 percent will not contain the true population mean number of visits per week

The State Education Department requires local school districts to keep these records on all students age race or ethnicity days absent current grade level standardized test scores in reading and mathematics and any disabilities or special educational needs the student may have Which of the following are categorical qualitative variables in these records Select all correct answers Days Absent O Race or Ethnicity Age Mathematics Test Score Disabilities or Special Needs Reading Test Score

Rewrite this number in appropriate scientific notation 0 0000875 answer

Compute the exact values 3 3 5

Evaluate 24

Evaluate 6 32 8 3 2

Estimate the V139 Pick the closest estimate 011 0 11 5 011 2 012 O 11 8

Round 9 2506 to the nearest thousandth

K question from a survey was How many credit cards do you currently have The results of the survey are provided Complete parts a through g below Click the icon to view the survey results a Determine the mean number of credit cards based on the raw data The mean is credit cards Type an integer or a decimal Do not round Credit Card Survey Results 3 2 3 2 5 2 3 2 2 5 2 2 2 10 3 2 2 3 8 2 10 3 3 3 3 3 3 2 4 4 2 2 3 8 2 2 7 5 3222 v w w c 3 3 1 3 2 5 1 4 2 1542 33 3 324237 N3 5332TNN 3423 2162 3 3 3 9 2 4 1 O X

Determine the required value of the missing probability to make the distribution a discrete probability distribution P 4 Type an integer or a decimal X 3 4 LO 5 6 P x 0 24 0 37 0 23

In the following probability distribution the random variable x represents the number of activities a parent of a K to 5th grade student is involved in Complete parts a through f below X P x 0 1 0 446 0 063 between 0 and 1 inclusive a Verify that this is a discrete probability distribution This is a discrete probability distribution because the sum of the probabilities is less than or equal to 1 2 3 t 0 276 0 137 greater than 0 and less than 1 4 0 078 and each probability is

12 Find the value that locates an area a in the upper tail of the F distribution that is fi or the following values of a and degrees of freedom a 05 df 6 df 45 b a 025 df 8 df 55 c a d a e a f a 01 df 7 df 38 10 df 12 df 87 005 df 7 df 46 001 df 15 df 58

Suppose the true proportion of voters in the county who support a restaurant tax is 0 48 Consider the sampling distribution for the proportion of supporters with sample size n 139 What is the mean of this distribution 0 48 What is the standard error of this distribution

3 cic Estimation and Tests for Comparing Two Population Variances 7 11 Find the value that locates an area a in the upper tail of the F distribution that is find Fa for the following values of a and degrees of freedom a a 05 df 7 df 9 b a 025 df 9 df 7 C a 01 df 17 df 9 d a 10 df 9 df 20 e a 25 df 15 df 12 f a 15 df 15 df 19

3 Find the following percentiles for a chi square distribution with df a X 05 b X 01 C X 95 d X 025 e X 03 f v

7 2 Suppose a random variable W has a chi square distribution with df 23 Determine th following probabilities a P W 41 64 b P W 35 17 c P W 13 09 d P W12 14 e P W 35 17 f P 12 14 W 35 17

55 57 596d 63 p 203 205 3 5 6 11cd 13d 1 A study was done on the relationship between high school grade point average GPA and scores on the SAT The following 8 scores were from a random sample of students taking the exam GPA SAT 3 2 725 3 8 752 3 9 745 3 3 680 b Interpret the residual that you calculated in part a B 3 6 700 The least squares regression line for predicting SAT from GPA was calculated to be y 154 158x a Calculate the residual for the student who had a GPA of 3 2 C P value 0 1974 2 8 562 2 Which residual plot below indicates that the linear model is appropriate Justify your answer A D friend 2 9 595 Dependent variable is Other R squared 87 3 s 3 853 with 11 2 9 degrees of freedom Variable Coefficient SE Coeff t ratio Intercept 306780 1 39 7 85 0 0001 2204 Marijuana 0 615003 0 0784 b Identify and interpret the coefficient of determination 3 5 730 3 The European School Study Project on Alcohol and Other Drugs published in 1995 investigated the use of marijuana and other drugs Data from 11 countries are summarized in the following scatterplot and regression analysis They show the association between the percentage of a country s ninth graders who report having smoked marijuana and who have used other drugs such as LSD amphetamines and cocaine c Identify and interpret the standard deviation of the residuals s a Write the equation of the least squares regression line

The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph The percentage of starting salaries falling above those shown by any rectangular bar is equal to the percentage of starting salaries falling below the bar Choose the correct answer below of Graduates Frequency 400 300 200 100 0 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars A False because this is only true if there is an even number of bars O B False because this is not true for any rectangular bar C True because the percentage of starting salaries falling below and above each bar must sum to 100 D True because this is true when there is odd number of bars

Here are summary statistics for randomly selected weights of newborn girls n 36 x 3216 7 g s 688 5 g Use a confidence level of 99 to complete parts a through d below a Identify the critical value f 2 used for finding the margin of error 2 2 72 Round to two decimal places as needed b Find the margin of error E 312 6 g Round to one decimal place as needed c Find the confidence interval estimate of 2904 1 g 3529 3 g Round to one decimal place as needed d Write a brief statement that interprets the confidence interval Choose the correct answer below OA One has 99 confidence that the sample mean weight of newborn girls is equal to the population mean weight of newborn girls OB There is a 99 chance that the true value of the population mean weight of newborn girls will fall between the lower bound and the upper bound OC Approximately 99 of sample mean weights of newborn girls will fall between the lower bound and the upper bound OD One has 99 confidence that the interval from the lower

The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph More college graduates had starting salaries in the 61 000 65 000 range than in the 46 000 50 000 range Choose the correct answer below of Graduates Frequency 400 300 200 100 0 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars A True because the bar for 61 65 is taller than the bar for 46 50 B True because the sum of the heights of the first two bars in the graph is greater than the sum of the heigh of the last two bars C False because the bar for 61 65 is shorter than the bar for 46 50 O D False because the bar for 61 65 has the same height as the bar for 46 50

Riches Click the icon to view the bar graph Choose the correct answer below OA The images in front of or behind each bar make it look as though the bars are taller than they really are OB The scale of the vertical axis makes the differences in bar height look larger than they really are C The wrong impression has been created about how the data are changing because equally spaced interval are not used on the horizontal axis O D The bars are not scaled proportionately in terms of the data they represent Average Weekly Pay on Selected Sports Teams E

Determine whether the statement makes sense or does not make sense and explain your reasoning The graph shown below indicates that for the period from 2016 to 2019 the percentage of Americans whose educational attainment was high school graduate has rapidly increased of HS Graduates or More Educational Attainment in the United States 90 2 90 0 89 8 89 6 89 4 89 2 89 0 88 8 2015 2016 2017 2018 Year 2019 more Choose the correct answer below OA Yes the statement makes sense B No it does not make sense the time interval on the horizontal axis creates an overall impression of the percentage of Americans with a high school education or better increasing rapidly OC No it does not make sense the percentage of Americans with a high school education or better increased more rapidly during the period from 2015 2016 D No it does not make sense the scale on the vertical axis is stretched to create an overall impression of the percentage of Americans with a high school education or better increasing rapidly

Describe what is misleading in the visual display of data below World Population in Billions 12 3 4 5 6 1804 1927 1960 1974 1987 1999 7 2012 2026 2043 Choose the correct answer below OA Time intervals on the horizontal axis do not represent equal amounts of time B The bars on the vertical axis curve around the globe instead of being on a straight line OC Part of the time frame on the horizontal axis of the graph has been cut off D The title does not explain what is being displayed

Describe what is misleading in the visual display of data below Marijuana Use Among College Students in the Last 30 Days Never Used 29 3 Not in Last 30 Days 10 Used 1 9 Days 5 5 Used 10 29 Days 3 5 Used All 30 Days 1 7 Choose the correct answer below O A The percentages do not add up to 100 B Colors on the chart are too light and distort the data C The chart is too small D The title does not explain what is being displayed

A questionnaire was given to students in an introductory statistics class during the first week of the course One question asked How stressed have you been in the last 2 weeks on a scale of 0 to 10 with 0 being not at all stressed and 10 being as stressed as possible The students responses are shown in the frequency distribution How many students were involved in the study Click the icon to view the frequency distribution students Type a whole number requency Distribution Stress Rating Frequency 6 4 1 20 15 12 0 1 2 3 4 5 6 7 8 1222 20 27 X

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the grouped frequency distribution to the right Among the classes with the greatest frequency which class has the least number of social interactions Choose the correct answer below A 25 29 C 55 59 OE 45 49 OG 10 14 O I 50 54 B 35 39 D 30 34 OF 40 44 OH 20 24 OJ 15 19 Number of Social Interactions 10 14 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 Frequency 9 19 19 19 9 8 8 8 1 4