Statistics Questions

1 point The scores of eight students who recently took both the PSAT and SAT exams are listed in the following table PSAT 183 207 167 206 197 142 193 176 SAT 2240 2080 1930 2420 2330 2110 2410 2020 Using statistical techniques which we ll study later it can be shown that the line of best fit for this data set has the formula y 4 56x 1354 where y represents a student s score on the SAT and a represents the same student s score on the PSAT Suppose a new student scores 176 on the PSAT What does the formula predict their score will be on the SAT Suppose a different student scores 1910 on the SAT What does the formula predict their score would be on the PSAT

Certified childcare providers for children ages 0 3 years exposed Office staff not exposed Total Disease 50 9 59 No Disease 950 891 1 841 Total 1000 900 1 900 Risk R Risk among the exposed R Risk among the unexposed a What is the 1 year risk cumulative incidence of disease for the exposed per 1 000 population Hint you will not need a calculator to get the answer R Risk among the exposed

CHECK IN DAY Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total Monday Tuesday Wednesday Thursday Friday Saturday Sunday MONDAY 40 Utilization 40 80 JP JP JP JP SP SP TUESDAY 40 40 96 40 120 WEDNESDAY 40 40 40 120 For example the first row of the table shows that 40 people checked in on Monday and were in the hospital for Monday Tuesday and Wednesday nights before being discharged on Thursday By summing the column of the table for Wednesday we see that there are 120 patients staying in the hospital that night How well is the hospital currently utilizing its beds Round your answers to 1 decimal place QUIRED THURSDAY FRIDAY 40 40 40 120 40 40 80 SATURDAY SUNDAY 40 40 40 40 A

A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage The pharmacist expects to sell 4800 packages of this antibioti at a steady rate during the next year She plans to place several orders of the same size spaced equally throughout the year The ordering cost for each delivery is 12 and carrying costs based on the average number of packages in inventory amount to 8 per year for one package Use this information to answer the following questions a Let x be the order quantity and r the number of orders placed during the year Find the inventory cost ordering cost plus carrying cost in terms of x and r C 12r 4x b Find the constraint function rx 4800 Type an equation c Determine the economic order quantity that minimizes the inventory cost and then find the minimum inventory cost 4 X

A rectangular corral of 216 square meters is to be fenced off and then divided by a fence into two sections as shown in the figure on the right Find the dimensions of the corral so that the amount of fencing required is minimized X meters W meters H

A certain airline requires that rectangular packages carried on an airplane by passengers be such that the sum of the three dimensions is at most 165 centimeters Find the dimensions of the square ended rectangular package of greatest volume that meets this requirement The length of the square end edge is The package length is cm cm ACCEID

Find the minimum of Q 3x 5y2 if x y 8 The minimum value of Q is Q Simplify your answer Type an exact answer using radicals as needed

Foggy Optics Inc makes laboratory microscopes Setting up each production run costs 2400 Insurance costs based on the average number of microscopes in the warehouse amount to 10 per microscope per year Storage costs based on the maximum number of microscopes in the warehouse amount to 10 per microscope per year Suppose that the company expects to sell 4000 microscopes at a fairly uniform rate throughout the year Determine the number of production runs that will minimize the overall expenses for the company The number of runs is

A cable runs along the wall from C to P at a cost of 10 per meter and straight from P to M at a cost of 26 per meter Let x be the distance from C to P If M is 24 meters from the nearest point A on the wall where P lies and A is 53 meters from C find x such that the cost of installing the cable is minimized and find this cost 53 X P A 24 M The cost is minimized when x is meters

A California distributor of sporting equipment expects to sell 10 800 cases of tennis balls during the coming year at a steady rate Yearly carrying costs to be computed on the average number of cases in stock during the year are 10 per case and the cost of placing an order with the manufacturer is 60 a Find the inventory cost incurred if the distributor orders 300 cases at a time during the year b Determine the economic order quantity that is the order quantity that minimizes the inventory cost Let x be the number of cases per order and r the number of orders placed per year If C represents the inventory cost then the objective equation is C equation is rx Do not include the symbol in your answer Or x The constraint

Find the dimensions of a closed rectangular box with a square base and volume 3375 in that can be constructed with the least amount of material What are the dimensions of the box The length of one side of the base is in

that the Relative extreme points exist when 8x has no relative extreme points In this case because the function f x 3x 2x 8x has no relative extreme points has multiple y intercepts has no x intercepts has multiple x intercepts has no y intercepts

Sketch the graph of the following function 5 f x x 9x 9x 3 Choose the correct graph below O A OB O C W D

Sketch the graph of the following function for x 0 4 X y x 7 4 O A 14 30 X 30 OB Ay 30 X 30 5 O C Ay 20 15 X oo Q G OD 15 20 X 30

Find the x intercepts of the given function y x 13x 39 The x intercept s is are Type an exact answer using radicals as needed Type an ordered pair Use a comma to separate answers as

Sketch the graph of the following function f x x 20x Choose the correct graph below O A X Q OB K M O C G D 150 Ay X 0

Sketch the following curve indicating all relative extreme points and inflection points y x 3x 7 The relative extreme points are Type an ordered pair Use a comma to separate answers as needed

The graph of the function has one relative extreme point Plot this point and check the concavity there Using only this information sketch the graph f x 2x 8 The relative extreme point on the graph is Type an ordered pair

Click the icon to view the frequency distributions Complete the relative frequency table below Relative Frequency Filtered Relative Frequency Nonfiltered 1 Tar mg 6 9 10 13 14 17 18 21 22 25 26 29 30 33 Simplify your answers 1 1 utions shown below then compare the amounts of tar in nonfiltered and filte Frequency Distributions Tar mg in Nonfiltered Cigarettes Frequency 14 17 1 18 21 1 14 7 2 22 25 26 29 30 33 Tar mg in Filtered Cigarettes 6 9 10 13 14 17 18 21 Frequency 2 1 5 17

A personal trainer is analyzing their clients data and created the chart below The trainer recorded the heights in inches I and weights in points y of 30 clients Use Excel to find the best fit linear regression equation Round the slope and intercept to two decimal places X 59 61 64 63 65 60 70 68 69 y 114 130 126 154 156 132 179 189 201

An organization collects information on the life expectancy in years of a person in certain countries and the fertility rate Der woman in those countries The data for 21 randomly selected countries for the year 2011 is given below Use Excel to Find the best fit linear regression equation where fertility rate is the explanatory variable Round the slope and intercept to wo decimal places Fertility Rate 2 1 N 2 7 3 2 2 6 6 1 5 4 in 7 5 1 4 Life Expectancy 71 1 67 8 70 6 66 1 67 6 55 3 82 7 57 5 75 9

The table below gives the average weight in kilograms of certain people ages 1 20 Use Excel to find the best fit linear regression equation where age is the explanatory variable Round the slope and intercept to two decimal places Age 1 2 3 4 5 01 6 8 9 Weight 9 2 12 0 14 2 15 4 17 9 19 9 22 4 25 8 28 1

An economist is studying the link between the total value of a country s exports and that country s gross domestic product or GDP The economist recorded the GDP and Export value in millions of s for 30 nations for the same fiscal year This sample data is provided below Help GDP 225274 297106 1470543 511685 930808 261974 542857 331360 703318 Exports 214010 205300 189700 188300 184300 180500 152000 151100 148400 Copy to Clipboard Download CSV 11

Data is collected on the relationship between the average number of minutes spent exercising per day and math test scores The data is shown in the table and the line of best fit for the data is 0 42x 64 6 Assume the line of best fit is significant and there is a strong linear relationship between the variables Provide your answer below Minutes 25 30 35 40 The predicted test score is Test Score a According to the line of best fit what would be the predicted test score for someone who spent 38 minutes exercising Round your answer to two decimal places 75 77 80 81

a b c Part 1 of 3 Refer to the graph at the right to answer the following questions At which labeled points is the function increasing At which labeled points is the graph concave up Which labeled point has the most positive slope The function is increasing at the labeled point s Use a comma to separate answers as needed B C D E y f x X E

In 2022 the CDC published data on the average weight of American female children by year Using ages 1 7 of this data researchers made a linear regression with age in years as the variable and weight in pounds as the y variable The equation of the line of best fit is 5 78x 17 56 According to the line of best fit what would you predict the weight would be for a 14 year old female Is it reasonable to use this line of best fit to make this prediction Select the correct answer below The predicted weight is 124 75 and the estimate is reliable and reasonable The predicted weight is 124 75 and the estimate is less reliable and unreasonable The predicted weight is 124 75 and the estimate is less reliable and reasonable The predicted weight is 98 48 and the estimate is reliable and reasonable O The predicted weight is 98 48 and the estimate is less reliable and reasonable O The predicted weight is 98 48 and the estimate is less reliable and unreasonable

Suppose melting snow causes a river to overflow its banks and h t is the number of inches of water on Main Street t hours after the melting begins a If h 150 4 by approximately how much will the water level change during the next hour and a half b Which of the following two conditions is better news for the next hour i h 150 7 h 150 6 h 150 10 ii h 150 7 h 150 6 h 150 10 In the next hour and a half the water level will change by inches Type an integer or a simplified fraction

The number of farms in the United States t years after 1925 is f t million where f t is graphed in Figure A and f t and f t are graphed in Figure B Click the icon to view Figure A Click the icon to view Figure B a Approximately how many farms were there in 1975 million farms Type an integer or decimal rounded to the nearest tenth as needed Figure A 6 5 4 3 2 1 Y 0 1925 10 20 y f t 30 40 50 a 60 70 t

Marilyn is studying the relationship between the time spent studying per day and the time spent reading per day and has collected the data shown in the table The line of best fit for the data is y 0 18x 36 8 Assume the line of best fit is significant and there is a strong linear relationship between the variables Studying Minutes Reading Minutes 60 80 100 120 48 51 54 59 a According to the line of best fit what would be the predicted number of minutes spent reading for someone who spent 180 minutes studying Round your answer to two decimal places a pooded

The table shows data collected on the relationship between age in years and daily time spent on the phone The line of best fit for the data is y 0 68z 95 6 Assume the line of best fit is significant and there is a strong linear relationship between the variables Age Years 30 40 50 60 Provide your answer below Minutes on the Phone 75 69 61 55 a According to the line of best fit what would be the predicted number of daily minutes spent on the phone for a person who is 27 years old Round your answer to two decimal places

Suppose that a large controlled experiment tests whether caffeine improves reaction times A very large number of randomly selected participants are randomly given identical seeming pills with varying doses of caffeine including none and then given tests of reaction times under the same conditions The experiment finds a strong negative correlation between caffeine dose and reaction time Note that lower reaction times are better Identify what can be concluded based on this information Select the correct answer below There is evidence that caffeine causes lower better reaction times People with lower better reaction times generally choose to consume more caffeine Lower reaction times are associated with higher caffeine doses but this study provides no evidence that caffeine causes lower reaction times There is no relationship between reaction time and caffeine E PASSTE

Identify the relation between caffeine consumption and sleep duration Select the correct answer below O Caffeine consumption and sleep duration are correlated O An increase in caffeine consumption causes a decrease in sleep duration O A decrease in sleep duration causes an increase in caffeine consumption O There is no relation between caffeine consumption and sleep duration

the more rashes you get Identify the relation between eating mangoes and rashes Select the correct answer below O Eating mangoes and rashes are negatively correlated O An decrease in eating mangoes causes an decrease in rashes O Correlation does not prove causation An increase in rashes causes an increase in eating mangoes

A survey regarding truck engines found a positive correlation between the size of the engine and horsepower the engine produces Fill in the blanks below based only on this information Provide your answer below It be concluded that trucks with larger engines have greater horsepower because A

Won a free ride to four years of college During these four years Jenn could also do any number of things including 1 Travel the world II Work to gather savings and career experience III Become a professional dancer Which of the following is the opportunity cost of Jenn attending college a Zero b Il only c The sum of I II III and any other opportunities she passed up d Whichever of I II III or any other opportunities she passed up is most valuable to her

the rkinson s Disease Activity we demonstrated two important statistical tools Experimentation Simulation How would you best describe these two tools Experiment D

11 Suppose the society produces one good corn using corn seed and labor Suppose they produce 500 bushels of corn output per year using 50 corn seed and 400 bushels of corn food to feed population and reproduce the labor force How much is the economic surplus in that society After that if 10 bushels of the corn surplus were added to the existing seed bin all other things remaining the same then 60 bushel of corn seed would produce 600 bushel of corn output with technology and population being same as before How much is the economic surplus in that society after using surplus to increase the size of the inputs

4 Interpret the production function Y f N L K 5 What causes economic growth

15 What are the three roles of prices in a market system

6 What are the two economic problems that have faced our societies and briefly explain each problem

8 What are the three economic systems in history and what is the main institution that governs an economy in each system

7 Why does distribution matter

A business finds that sales increase when the outdoor temperature decreases Identify the relation between sales and temperature Select the correct answer below O Sales and temperature are positively correlated An increase in sales causes an increase in temperature O Sales and temperature are negatively correlated An increase in temperature causes an increase in sales

Choose all of the true statements below Select all that apply The more coffee a person drinks the taller they are The higher the outside temperature the fewer hot chocolate sales a store will have The fewer absences a student has the higher their grade The more someone brushes their teeth the less cavities they have

Suppose you computed T 0 493 using n 52 data points Using the critical values table below determine if the value of IN Tis significant or not df 3 4 5 6 7 8 9 10 CV and 0 997 0 950 0 878 0 811 0 754 0 707 0 666 0 602 0 576 Select the correct answer below df 11 12 13 14 16 17 18 19 20 CV and 0 555 0 532 0 514 0 497 0 482 0 468 0 456 0 444 0 433 0 423 df 21 22 23 24 25 26 27 28 29 30 CV and df 0 413 40 0 404 0 396 0 388 0 381 0 374 0 367 0 361 0 355 0 349 Oris significant because it is between the positive and negative critical values Or is not significant because it is between the positive and negative critical values Oris significant because it is not between the positive and negative critical values T is not significant because it is not between the positive and negative critical values 50 60 70 80 90 100 CV and 0 304 0 273 0 250 0 232 0 217 0 205 0 195

True or false Increases in height cause increases in shoe size Select the correct answer below True False

Three students are planning a road trip for Spring Break There are two paths available to their destination and they choose the shorter road because the longer a road the greater the amount of time it will take to travel its length Assume speed is constant Fill in the blanks below based only on this information Provide your answer below It be concluded that the longer a road the greater the amount of time it will take to travel its length because

all community college employs 128 full time faculty members To gain the faculty s opinions about upcoming contract negotiations the president of the faculty union wishes to obtain a simple random sample that will consist of 5 faculty me bers the faculty 1 to 128 StatCrunch with a single fixed seed of 45 to obtain a simple random sample of 5 faculty members Write the numbers corresponding to the members below First faculty member Second faculty member Third faculty member Fourth faculty member Fifth faculty member U 01 COCTED

A non profit finds that donations decrease when the economy measured by GDP decreases Identify the relation between donations and GDP Select the correct answer below O Donations and GDP are positively correlated Donations and GDP are negatively correlated A decrease in donations causes a decrease in GDP A decrease in GDP causes a decrease in donations

Opening Activity 13 A researcher surveyed 80 adults and found that 22 regularly run for exercise and 18 regularly swim The probability that they both run and swim is What is the probability that they run or swim 1