Statistics Questions

Which histogram depicts a higher standard deviation Frequency 10 8 6 0 30 40 50 60 70 a Choose the correct answer below Frequency 10 8 2 0 40 44 48 52 56 60 b Q Q Q OA Histogram a depicts the higher standard deviation B Histogram b depicts the higher standard deviation since it is more bell shaped because the distribution has more dispersion OC Histogram b depicts the higher standard deviation O D Histogram a depicts the higher standard deviatio because the bars are higher than the average bar because the distribution has more dispersion in a

In a statistics class the standard deviation of the heights of all students was 3 8 inches The standard deviation of the heights of males was 3 4 inches and the standard deviation of females was 3 3 inches Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately Choose the correct answer below COL OA The distribution of the heights for the entire class generally has more spread than the distribution of the heights of the individual sexes OB The smaller sample size results in a smaller sample standard deviation OC There is more dispersion in the heights of the male and female samples than the heights of the entire class OD The sample sizes of the male students and female students are less than the sample size of the entire class

Over the past 10 years five mutual funds all had the same mean rate of return The standard deviations for each of the five mutual funds are shown below Capital Investment 8 8 Vanity 11 1 Global Advisor 10 2 International Equities 9 3 Nomad 6 4 Which mutual fund was least consistent in rate of return This is a reading assessment question Be certain of your answer because you only get one attempt on this question Choose the correct answer below OA Global Advisor O B Capital Investment OC Nomad OD International Equities O E Vanity

True or False When comparing two populations the larger the standard deviation the more dispersion the distribution has provided that the variable of interest from the two populations has the same unit of measure Choose the correct answer below C O A True because the standard deviation describes how far on average each observation is from the typical value A larger standard deviation means that observations are more distant from the typical value and therefore more dispersed OB False because the standard deviation measures the spread of the distribution not the dispersion of the distribution OC False because the larger the standard deviation is the less dispersion the distribution has OD True because the standard deviation is the difference between the largest and smallest observation When the standard deviation is larger there is more distance between the largest and smallest observation and therefore more dispersion in the distribution

Find the payment necessary to amortize a 12 loan of 2100 compounded quarterly with 17 quarterly payments The payment size is Round to the nearest cent www

If the variance of a variable is 36 what is the standard deviation This is a reading assessment question Be certain of your answer because you only get one attempt on this question The standard deviation is Type an integer or decimal rounded to two decimal places as needed

What can be said about a set of data with a standard deviation of 0 This is a reading assessment question Be certain of your answer because you only get one attempt on this question Choose the correct answer below O A For every positive value there is a corresponding negative value as in 4 and 4 6 and 6 OB All the observations are the same value OC All the observations are 0

Identify the given statement as either true or false The standard deviation can be negative This is a reading assessment question Be certain of your answer because you only get one attempt on this question Choose the correct answer below False O True

True or False Chebyshev s inequality applies to all distributions regardless of shape but the empirical rule holds only for distributions that are bell shaped Choose the correct answer below O A True Chebyshev s inequality is less precise than the empirical rule but will work for any distribution while the empirical rule only works for bell shaped distributions OB False both Chebyshev s inequality and the empirical rule will only work for bell shaped distributions OC False both Chebyshev s inequality and the empirical rule will work for any distribution O D False the empirical rule is less precise than Chebyshev s inequality but will work for any distribution while Chebyshev s inequality only works for bell shaped distributions

Let be the number of packages being mailed by a randomly selected customer at a certain shipping facility Suppose the distribution of X is as follows 2 3 4 p x 0 2 0 4 0 1 0 3 X X a Consider a random sample of size n 2 two customers and let X be the sample mean number of packages shipped Obtain the probability distribution of X 1 1 5 2 2 5 3 3 5 P X 0 04 1 0 6 0 16 b Refer to part a and calculate P X 2 5 0 3 0 2 0 28 0 2 2 c Again consider a random sample of size n 2 but now focus on the statistic R the sample range difference between the largest and smallest values in the sample Obtain the distribution of R Hint Calculate the value of R for each outcome and use the probabilities from part a R 0 1 3 P R 0 3 0 25 0 12 0 06 0 09 4 d If a random sample of size n 4 is selected what is P X 1 5 Hint You should not have to list all possible outcomes only those for which x 1 5

Find the amount necessary to fund the given withdrawals Quarterly withdrawals of 600 for 6 years interest rate is 4 7 compounded quarterly The amount necessary to fund the given withdrawals is Round to the nearest cent as needed www

The annual profits of five large corporations in a certain area are given below Which measure of central tendency should be used 206 000 214 000 234 000 204 000 1 284 000 OA mean B midrange C median OD mode

K The table below shows a random sample of 30 quantitative SAT scores of first year students admitted at a university Make an appropriate graph of distribution of the data and describe the distribution 655 559 734 653 651 541 672 666 688 641 577 732 679 616 557 535 665 727 669 610 530 708 732 793 0 688 676 624 600 652 723 C The distribution appears to be left skewed D The distribution cannot be determined Identify any outlier s Select the correct answer below and if necessary fill in any answer box to complete your choice OA There is more than one outlier They are scores of Use a comma to separate answers as needed OB There is one outlier It is a score of OC There are no outliers in the data set

Provide an appropriate response In interpreting a boxplot of a data set we note that the median is to the left of the center of the box and the right line is longer than the left line We can conclude that OA The data is skewed right B The data is skewed left C The data is symmetric D Skewner mot

Construct a frequency distribution for the data using five classes Describe the shape of the distribution The data set Pick Three Lottery Outcomes for 10 Consecutive Weeks 3 676061784 1 5 7 5 9 1 5399 2230884024 OA bell shaped B uniform C skewed to the left D skewed to the right

F According to an organization there are five leading causes of preventable death in a region They are shown in the graph to the right where HBP is High Blood Pressure TU is Tobacco Use HBG is High Blood Glucose PA is Physical Activity and OO and Overweight and Obesity Use the graph to complete parts a through e a Estimate how many preventable deaths result from high blood pressure Approximately million preventable deaths in one year result from high blood pressure Round to one decimal place as needed Millions in One Year PIN WAGON HBP TU HB

SAS was used to compare the high school dropout rates for the 30 school districts in one city in 2010 and 2012 The box plots generated for these dropout rates are shown below Compare the center of the distributions and the variation of the distributions for the two years 49 25 36 9375 24 625 12 3125 0 Variable RATE n

The bar graph below shows the political party affiliation of 1000 registered U S voters What percentage of the 1000 registered U S voters belonged to one of the traditional two parties Democratic and Republican Percentage 40 30 20 10 0 Democrat Republican Independent Other Party Affiliation OA 40

A farmer wishes to test the effects of a new fertilizer on her corn yield She has four equal sized plots of land one with sandy soil one with rocky soil one with clay rich soil and one with average soil She divides each of the four plots into three equal sized portions and randomly labels them A B and C The four A portions of land are treated with her old fertilizer The four B portions are treated with the new fertilizer and the four C s are treated with no fertilizer At harvest time the corn yield is recorded for each section of land What is the response variable in this experiment OA the four types of soil B the type of fertilizer old new or none OC the section of land A B or C D the corn vield recorded for each section of land

Explain what is misleading about the graphic The volume of our sales has doubled OA The length of a side has doubled but the area has been multiplied by 4 B The graphic is not misleading C The length of a side has doubled but the area has been unchanged D The length of a side has doubled but the area has been multiplied by 8

Provide an appropriate response Given the following five number summary find Q3 2 9 5 7 10 0 13 2 21 1 OA 21 1 OB 13 2 C 10 0 D 57

of 1 Macmillan Learning Use the Statistical Applet The Reasoning of a Statistical Test to answer the question Click NEW SHOOTER then have the new shooter take 5 shots Observe the percentage of hits Now have the same shooter take 10 more shots for a total of 15 Again observe the percentage of hits Finally have the same shooter take at least 35 more shots for a total of 50 or more Observe the percentage of hits Click the Show true probability checkbox to reveal the true probability of hitting a free throw for this shooter Do you feel that the evidence you have seen here allows you to reject the null hypothesis that the shooter makes 80 of all his free throws Do you think it is better to make this decision after seeing 5 15 or 50 shots Select the true statements T It is certainly better to make a decision after seeing 5 shots than after seeing 15 or 50 shots One thing this applet demonstrates is that even after many many observations it is still impossible to know for sure whether or not a null hypothesis should be rejected It is certainly better to make a decision after seeing 15 shots than after seeing 5 or 50 shots It is certainly better to make a decision after seeing 50 shots than after seeing 5 or 15 shots The less shots we see the shooter take the larger the sample size we have to estimate the shooter s true underlying

Provide an appropriate response Over the fast 10 years four mutual funds all had the same mean rate of return 12 These mutual funds had different standard deviations as follows Mutual Money 8 Co joined Investments 6 Together Fund 4 All for One Fund 9 Which mutual fund investment is the most consistent in rate of return OA Co joined Investments B All for One Fund C Together Fund D Mutual Money

Describe the shape of the distribution Relative Frequency OA skewed to the right B uniform OC skewed to the left

You are asked to compare three data sets Without calculating determine which data set has the greatest sample standard deviation and which has the least sample standard deviatio Click here to view the data sets OA Greatest sample standard deviation 1 Least sample standard deviation iii OB Greatest sample standard deviation ii Least sample standard deviation i OC Greatest sample standard deviation i Least sample standard deviation ii OD Greatest sample standard deviation i Least sample standard deviation ii Data Sets 0 14 15 11 H 14 iii 15 16 17 18 19 16 17 18 19 4

If nothing is known about the shape of a distribution what percentage of the observations fall within 2 standard deviations of the mean OA approximately 5 OB at most 25 OC C approximately 95 D at least 75

K Match the description of the sample with the correct plot Time in minutes it takes a sample of employees to drive to work O A Key 09 0 9 0 9 1 49 2 3678 3 01568 4 OC 5 0 10 15 20 25 30 35 40 45 D O B Key 7 2 72 6 89 7 8 9 OD 0233678 2456778 0115 200 205 210 215

The Excel frequency bar graph below describes the employment status of a random sample of U S adults What is the percentage of those having no job sets or no job 2 part time jobs 1 part time job 1 full time job A 40 B 15 0 Frequency Bar Graph 5 6 8 10 10 15 16 20

The February utility bills in dollars for ten residents of a large city are listed below Find the mode amount 71 67 67 72 76 72 73 68 72 72 OA 76 OB 73 C 67 D 72

Provide an appropriate response The government of a town needs to determine if the city s residents will support the construction of a new town hall The government decides to conduct a survey of a sample of the city s residents Which one of the following procedures would be most appropriate for obtaining a sample of the town s residents A Survey every 8th person who walks into city hall on a given day B Survey a random sample of employees at the old city hall C Survey a random sample of persons within each geographic region of the city D Survey the first 300 people listed in the town s telephone directory

Approximate the mean of the grouped data Round to the nearest whole number Phone calls per day Frequency 8 11 12 15 16 19 20 23 24 27 46 51355 11 43 OOO OO OA B

QUESTION 49 1 POINT Lexie gets 2 3 likes per day on average on a Facebook ad she pays for with a standard deviation of 0 7 She decided to see if using a new ad would decrease her average She used the new ad for 15 days For those 15 days Lexie got an average 1 9 likes She wants to know if the new ad reduced her number of likes each day Lexie conducts a one mean hypothesis at the 10 significance level to test if the new ad helped her get more likes each day Ho p 2 3 H p 2 3 which is a left tailed test Determine the test statistic rounded to two decimal places Provide your answer below test statistic

The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces andra standard deviation of 5 ounces 33 randomly selected people are surveyed Round all answers to 4 decimal places where possible a What is the distribution of X X N b What is the distribution of N c What is the probability that one randomly selected person drinks between 14 5 and 15 3 ounces of coffee per day d For the 33 people find the probability that the average coffee consumption is between 14 5 and 15 3 ounces of coffee per day e For part d is the assumption that the distribution is normal necessary Yes No

at is the most common trick to mislead readers of bar graphs pose the correct answer below A Change the color of the bars to make some categories appear more important than others B Change the width of the bars to make some categories appear more important than others C Change the scale of the vertical axis so that it does not start at 0 D Change the scale of the horizontal axis so that it does not start at 0

hat are two commonly used graphs to display the distribution of a sample of cate hoose the correct answer below Histograms and dotplots O Bar graph and pie chart O Dotplots and bar graphs Bar graph and stemplot

A fitness instructor measured the heart rates of the participants in a yoga class at the conclusion of the class The data is summarized in the histogram to the right There were fifteen people who participated in the class between the ages of 25 and 45 Use the histogram to answer the question How many participants had a heart rate between 120 and 120 bpm OA 4 OB 5 OC 2 OD 3 point s pos 90 100 110 129 130 140 150

The average number of miles in thousands that a car s tire will function before needing replacement is 72 and the standard deviation is 10 Suppose that 12 randomly selected tires are tested Round all answers to 4 decimal places where possible and assume a normal distribution a What is the distribution of X X N b What is the distribution of a N c If a randomly selected individual tire is tested find the probability that the number of miles in thousands before it will need replacement is between 76 and 79 3 d For the 12 tires tested find the probability that the average miles in thousands before need of replacement is between 76 and 79 3 e For part d is the assumption that the distribution is normal necessary Yes No

This question 1 point s possible K A student receives test scores of 62 83 and 91 The student s final exam score is 88 and homework score is 76 Each test is worth 20 of the final grade the final exam is 25 of the final grade and the homework grade is 15 of the final grade What is the student s final grade in the class A 90 6 OB 85 6 O C 76 6 OD 80 6 CHIB Submit

The graph below is an ogive of scores on a math test The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile Use the graph to approximate the percentile rank of an individual whose test score is 45 Q Percentile Ranks of Math Test Scores 100 90 80 70 60 50 40 30 20 104 0 0 10 20 30 40 50 60 70 80 90 100 Question 14 of 21 G EXIB This This OA 65 OB 60 O C 19 OD 14

K The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams Use z scores to determine which birth weight could be considered unusu O A 2000 g OB 1200 g OC 3647 g OD 2353 g

K uestion Find the z score for the value 90 when the mean is 59 and the standard deviation is 4 OA Z 7 50 OB z 7 75 OC z 1 46 OD z 1 46

This question 1 point s possible Many firms use on the job training to teach their employees computer programming Suppose you work in the personnel department of a firm that just finished training a group of its en you have been requested to review the performance of one of the trainees on the final test that was given to all trainees The mean and standard deviation of the test scores are 70 ar distribution of scores is bell shaped and symmetric Suppose the trainee in question received a score of 67 Compute the trainee s z score OA Z 1 50 OB Z 0 93 OC z 0 93 OD z 1 5 MIXE

Percentile The graph below is an ogive of scores on a math test The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile Use the graph to approximate the test score that corresponds to the 40th percentile Percentile Ranks of Math Test Scores 100 90 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Test Sccore Q a Question 15 of 21 E This quiz 21 This questio OA 15 OB 10 OC 62 OD 56

The mean score of a competency test is 80 with a standard deviation of 5 Use the empirical rule to find the percentage of scores between 75 and 85 Assume the data set has a bell shape OA 99 7 OB 95 OC 50 D 68 OOO

The heights in inches of 10 adult males are listed below Find the sample standard deviation Round to the nearest hundreth 70 72 71 70 69 73 69 68 70 71 OA 2 38 O B 70 O C 3 OD 1 49

K The mean IQ score of adults is 100 with a standard deviation of 15 Use the empirical rule to find the percentage of adults with scores between 70 and 130 Assume the data set has a bell sham distribution OA 68 OB 100 OC 99 7 OD 95

K Determine whether the approximate shape of the distribution in the histogram is symmetric uniform skewed left skewed right or none of these 20 18 16 14 12 10 8 6 4 2 L 25 000 45 000 65 000 85 000 This question 1 OA symmetric OB skewed right OC uniform OD skewed left

Use the ogive to the right to approximate the sample size O A 100 OB 341 O C 80 GILB This question 1 point s possible Aanba n mber of students 828898 Number of s 9882 Submit Leisure Time of College Students 95 14 5 19 5 24 5 25 Number of hou

4 Suppose X is a discrete random variable with possible values X 0 1 2 or 3 Suppose P X 0 0 08 P X 1 0 22 P X 2 0 36 and P X 3 0 34 Find the mean of X Do not round your answer Answer Continue Reset answer

Determine the original set of data 11 4 6 6 7 12 0 4 6 8 899 13 3 4 4 6 899 14 0 2 3 4 5 15 2 6 Legend 512 represents 5 2 Choose the correct answer below OA 11 4667 12 0468899 13 3446899 14 02345 15 26 OB 11 4 11 6 11 6 11 7 12 0 12 4 12 6 12 8 12 8 12 9 12 9 13 3 13 4 13 4 13 6 13 8 13 9 13 9 14 2 14 3 14 4 14 5 15 2 15 6 OC 114 116 116 117 120 124 126 128 128 129 129 133 134 134 136 138 139 139 140 142 1 145 152 156 OD 11 11 11 11 12 12 12 12 12 12 12 13 13 13 13 13 13 13 14 14 14 14 14 15 15