Statistics Questions and Answers

Test the claim that the mean of group 1 is less than the mean of group 2 Two samples are randomly selected and come from populations that are normal The sample statistics are given below Population 1 Population 2 Sample Size 15 15 Sample Mean 4 1 4 5 Sample SD 0 76 0 51 Use the significance level of 5 alpha 0 05 There is sufficient evidence to support the claim O There is not sufficient evidence to support the claim O There is not enough information to determine

1 A certain electric car company claims publicly that their car batteries will last for at least 300 000 miles An internal study done by the company showed that the lifespans of their car batteries followed a normal probability distribution with a mean lifespan of 400 000 miles and a standard deviation of 60 000 miles What percent of their car batteries will fail to meet the public claim of lasting at least 300 000 miles Round to the nearest tenth of a percent

7 Which of the following statements about z scores is are true Circle all that are true a larger z scores are always preferable b the z scores for an observation that is equal to the mean is 1 c if a z score is positive that means that the observation is less than the mean d if a z score is 1 that means that the ob servation is one standard deviation be low the value of the mean e none of the above are true

The PTO is selling raffle tickets to raise money for classroom supplies A raffle ticket costs 4 There is 1 winning ticket out of the 230 tickets sold The winner gets a prize worth 96 Round your answers to the nearest cent What is the expected value to you of one raffle ticket Calculate the expected value to you if you purchase 10 raffle tickets What is the expected value to the PTO of one raffle ticket If the PTO sells all 230 raffle tickets how much money can they expect to raise for the classroom supplies

A research group is interested in determining the proportion of commuters in a large city who travel by bus For a random sample of 270 commuters in the city it is found that 178 commuters travel by bus A 90 confidence interval for the population proportion is

Find the z score for the given shaded region under the standard normal distribution Round your answer to two decimal places 4 Shaded Area 0 67 3 2 1 0 Z 1 2 3 Q

In order to estimate the proportion of personal bankruptcies that are a result of medical bills a research group took a sample of 200 bankruptcy cases and counted 120 that resulted from medical bills A 99 confidence interval for the proportion of all personal bankruptcies that result from medical bills is about

The graph ates a norr istribut mean price paid is 1800 and the standard deviation is 95 1515 1610 1705 1800 1895 1990 2085 Distribution of Prices Q What is the approximate percentage of buyers who paid between 1800 and 1990 What is the approximate percentage of buyers who paid between 1705 and 1895 What is the approximate percentage of buyers who paid less than 1515 What is the approximate percentage of buyers who paid between 1705 and 1800 What is the approximate percentage of buyers who paid less than 1610 What is the approximate percentage of buyers who paid between 1515 and 1800

An economy is based on three sectors agriculture manufacturing and energy Production of a dollar s worth of agriculture requires inputs of 0 30 from agriculture 0 30 from manufacturing and 0 20 from energy Production of a dollar s worth of manufacturing requires inputs of 0 20 from agriculture 0 20 from manufacturing and 0 30 from energy Production of a dollar s worth of energy requires inputs of 0 20 from agriculture 0 40 from manufacturing and 0 40 from energy Find the output for each sector that is needed to satisfy a final demand of 10 billion for agriculture 32 billion for manufacturing and 54 billion for energy The output of the agricultural sector is billion dollars Round the final answer to three decimal places as needed Round all intermediate values to six decimal places as needed

vork Part B ssume the random variable x is r P 71 x 79

A pediatrician measured the heights of 22 randomly selected 6 year old girls The average height for these 6 year old girls is X 64 25 inches with a standard deviation S 6 25 Assuming that height is normally distributed a 95 confidence interval for u is

To estimate the mean retail price of designer jeans a buyer sampled 20 retailers in New York City and recorded the selling price of the jeans The following statistics were reported x 61 50 dollars and s 6 25 dollars Assuming the prices at different retailers are normally distributed a 90 confidence interval for the mean is closest to

A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week The responses are recorded in Table Use this sample data to construct a 93 confidence interval for the mean number of hours statistics students will spend watching television in one week Assume the population is normally distributed Give your answer to 3 decimal places if necessary 13 13 16 6 18 4 16 11 16 8 13 13 15 10 9

Find the determinant by row reduction to echelon form 1 0 1 4 1 85 1 66 0 7 7 4 39 0 Use row operations to reduce the matrix to echelon form 1 1 85 0 1 66 1 0 7 7 4 4 39 0

Linear Functions Fit to Data LC A company determines an employee s starting salary according to the number of years of experience as detailed in the table Years of experience Salary 42 150 44 280 46 785 48 820 51 126 1 2 3 4 5 Using technology determine the line of fit where x represents the number of years of experience and y represents the salary Oy 2525x 40000 Oy 2525x 40000 Oy 2233 3x 39940 Oy 2233 3x 39940

MOTEUTETTENT The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A Number of Years 16 18 Average Daily Temperature Jan 1 1900 1934 City A 20 22 24 26 Average Daily Temperature 28 30 The mean of the temperatures in the chart is 24 with sta 32

Which of the following describes the probability distribution below 0 5 045 64 0 35 03 0 25 02 0 15 01 0 00 0 Probability Distribution The median is greater than the mean and the majority of the data points are to the left of the me The median is greater than the mean and the majority of the data points are to the right of the m The mean is greater than the median and the majority of the data points are to the left of the me The mean is greater than the median and the majorit

The scores of the students on a standardized test are normally distributed with a mean of 500 and a standard deviation of 110 What is the probability that a randomly selected student has a score between 350 and 550 Use the portion of the standard normal table below to help answer the question Z 0 00 0 25 0 35 0 45 1 00 1 26 1 35 1 36 9 24 Probability 0 5000 0 5987 0 6368 0 6736 0 8413 0 8961 0 9115 0 9131

Destiny performs a hypothesis test on a population with u 115 and o 30 Her sample size is 25 with a mean of 120 4 Which of the following correctly depicts the z statistic for this data O 0 04 0 90 3 53 3 93

0 M 20 30 10 40 Which statement must be true 50 60 Each distribution has the same mean and the same standard deviation Each distribution has the same mean and a different standard deviation Each distribution has a different mean and the same standard deviation Each distribution has a different mean and a different standard deviation

Data were collected on the distance a hockey puck will travel when hit by a hockey stick at a certain speed The speed s is measured in miles per hour and distance is measured in yards The line of fit is given by 3 95 60 25s If a hockey player hits a puck at a speed of 50 miles per hour how far will the puck travel O3 016 45 yards

A business has a budget of 1 890 to spend on updating their technology Each month x the business spends 135 on various technology updates The amount of money remaining in the budget for technology T x can be described by the function T x 135x 1890 What is the interpretation of the x intercept in the context of the problem After 14 months the business will have 0 remaining in their technology budget OAfter 1 month the business will have 1 755 remaining for technology updates O The initial technology budget for the business is 1 890 The business spends 135 every month updating their technology

Linear Functions Fit to Data LC The scatter plot shows the number of households in millions that have cable television over eight consecutive years Number of Households 10 9 8 B 5 4 3 2 T 04 y 08 9 million 9 7 million 0 1 2 12 1 million Predict the number of households with cable television in year 12 3 5 Time Years 80x 4 6 7 8 9

Two Way Frequency Tables LC Music students and art students at a middle school were surveyed to choose a cardiovascular activity playing sports or dancing Do you prefer dancing or playing sports Music students 32 Art students 31 Column totals 63 15 Playing sports Dancing Row totals 47 53 22 37 15 22 What is the marginal frequency of students who chose dancing 37 100

A camping store purchases tents from the manufacturer for 175 The camping store then marks up the tents 40 to sell to their customers What price do the customers pay for the tents O 280 O 245 O 105 O 70

Jair orders a chicken burrito bowl for 6 84 a side of guacamole for 1 89 and a large fountain drink for 2 59 He wants to tip the server 20 How much money will Jair s tip be O 0 23 2 26 O 2 83

The hourly wage of a paramedic is 16 12 If the paramedic works 40 hours per week what is their salary each week O 112 84 161 20 4513 60

A businessperson is returning from a trip to China and has 470 72 yuan in their wallet The most current currency conversion rate is 1 U S dollar 6 4651 yuan How much money will the businessperson have when they convert their money to U S dollars O 3043 25 O 477 19 O 464 25

A university is interested in determining the average statistics anxiety score for all undergraduate students in the U S For a random sample of 59 undergraduate students it is found that the average average statistics anxiety score is 42 3 with a standard deviation of 0 7 Assume that the statistics anxiety scores for all undergraduate students in the U S is normally distributed A 95 confidence interval for the true mean statistics anxiety score is closest to

Given f x 6x 8 and g x 5x 2 what is f g x Ox 10 Ox 6 011x 10

Raven purchases a new cell phone for 800 that depreciates annually The value of her cell phone per year can be modeled by the exponential function f x 800 0 82 where x is the number of years What is the range of this exponential function in terms of the context of the problem 0 0 00 OR 800 00 4

Table shows a different random sampling of 20 cell phone models Use this data to calculate a 98 confidence interval for the true mean SAR for cell phones certified for use in the United States As previously assume that the population standard deviation is o 0 337 Phone Model Blackberry Pearl 8120 HTC Evo Design 4G HTC Freestyle LG Ally LG Fathom LG Optimus Vu Motorola Cliq XT Motorola Droid Pro DELET Nokia 7705 Twist MET DE CANA Motorola Droid Razr M SAR 1 48 0 8 1 15 1 36 0 77 0 462 1 36 1 39 1 3 0 7 Phone Model Nokia E71x Nokia N75 Nokia N79 Sagem Puma Samsung Fascinate Samsung Infuse 4G Samsung Nexus S Samsung Replenish Sony W518a Walkman ZTE C79 SAR 1 53 0 68 1 4 1 24 0 57 0 2 0 51 0 3 0 73 0 869

Measurement of the waiting time of 40 randomly selected patients at a hospital emergency room gave mean of 14 4 The population standard deviation is 5 5 A 95 confidence interval for the mean waiting rime of all patients is about

Suppose the following data set represents the running times for the 15 top grossing movies rated PG or PG 13 Find the five number summary Report the five number summary in the following order Min Q1 Median Q2 Q3 Max 110 121 90 108 108 106 91 128 162 90 113 120 120 102 129 Provide your answer below

4 Kenya pays 56 34 biweekly for health insurance which is 18 of the total cost Her employer pays the rest What is he employer s annual contribution for Kenya s health insurance

Review Third Nine 36 Cherie accepted a job through an employment agency The job pays 1 200 weekly The agency charges 22 of her first three months pay How much money will the employment agency receive for placing Cherie in her new job Roune to the nearest dollar

The estimate the current average retirement age of US citizens a researcher sampled 56 recently retired individuals The sample data yielded mean 64 7 years and standard deviations 0 6 year A 98 confidence interval for the true mean retirement age of all recently retired individuals is about DOOG 64 54 64 86 64 58 64 82 64 45 64 95 64 55 64 85 64 51 64 89

In a survey of 2321 adults from France 1703 said that they believed that the activities of humans are contributing to an increase in global temperatures A 95 confidence interval for the proportion p of adults in France who think humans are contributing to an increase in global temperatures is closest to 0 3329 0 5633 0 6639 0 9343 0 7158 0 7517 0 2726 0 8024 0 2148 0 3925

A standard deck of cards contains 52 cards One card is selected from the deck a Compute the probability of randomly selecting a four or nine b Compute the probability of randomly selecting a four or nine or queen c Compute the probability of randomly selecting a queen or diamond a P four or nine Round to three decimal places as needed b P four or nine or queen c P queen or diamond Round to three decimal places as needed Round to three decimal places as needed

Sixteen of the 100 digital video recorders DVRs in an inventory are known to be defective What is the probability you randomly select a DVR that is not defective The probability is

Question 11 Essay Worth 10 points Business Costs MC A company produces and sells solar panels for 520 The company s daily profit P x graph to answer the questions

Question 2 Multiple Choice Worth 4 points Calculating Net Worth LC The assets and liabilities of a lawyer are listed below Car Value Car Loan Savings Account Balance Season Baseball Tickets Student Loans Credit Card Balance Checking Account Balance Home Value What is the lawyer s net worth OS332 677 O 335 436 OS341 204 5373 113 25 023 10 892 32 543 5 768 15 089 5 928 2 125 307 654 3

Question 5 Multiple Choice Worth 4 points Business Costs LC Zion Sun Chairs manufactures 3 575 beach chairs each month Determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of 75 000 if the total monthly fixed costs are 17 363 50 and the variable cost per chair is 52 17 O 20 98 O 25 84 O 72 50 Asso01 R

Budgeting LC A high school teacher earns an average bi weekly net pay of 1 541 65 Which compound inequality correctly shows the amount of money m the teacher can spend if the monthly budget for entertainment is between 5 and 10 O 77 08 sms 154 17 O 154 17 sms 308 33 O 167 01 sms 334 02 O 200 41 sms 367 43

The profit P x that Rivka s Delivery Service makes from delivering packages between local businesses is P x where x is the number of 0 10 price increases for each delivery Use the graph below to answer the question profit 80 60 40 20 0 081 080 2 What is the approximate value for the maximum profit 50 4 6 number of price increases

are ducting a study to see if the mean doctor s salary in thousands of dollars is significantly more than 88 A random sample of 26 doctors salary in thousands of dollars is shown below Test the claim using a 1 level of significance Give answer to at least 4 decimal places Salary 90 55 94 03 84 83 87 4 96 03 82 76 95 22 87 28 94 52 92 33 92 12 84 36 87 02 94 2 88 22 87 92 87 98 94 12 89 12 89 74 77 69 78 05 93 15 88 03 81 72 95 88 a What are the correct hypotheses Ho Select an answer H Select an answer Based on the hypotheses find the following b Test Statistic c Critical value Shade Left of a value d Shade the sampling distribution curve with the correct critical value s and shade the critical regions The arrows can only be dragged to t scores that are accurate to 1 place after the decimal point these values correspond to the tick marks on the horizontal axis Select from the drop down menu to shade to the left to the right between or left and right of the t score s 214 1 5 thousand dollars 0 thousand dollars Click and drag the arrows to adjust the values e The correct decision is to Select an answer I

For a confidence level of 95 with a sample size of 11 find the critical t value

The mean work week for engineers in a start up company is believed to be about 65 hours A newly hired engineer hopes that it s shorter She asks 10 engineering friends in start ups for the lengths of their mean work weeks Their responses are 70 45 55 60 65 55 55 60 50 55 Is the newly hired engineer testing a mean or a proportion mean proportion The null hypothesis in symbols is Is the test left tailed right tailed or two tailed left tailed right tailed two tailed O

Select all that apply The t distribution can be used for inference when working with the standardized difference of two means if the samples are dependent each sample meets the conditions for using the t distribution the samples are independent

An unknown metal has been found and the following experimental results have been tabulated in the table below The table contains the grams of the unknown metal and the volume in milliliters of water displacement Find a linear model that expresses volume as a function of the mass grams Volume in ml 16 302 9 17 5 331 3 19 359 7 20 5 404 22 433 5 23 5 458 6 25 487 8 A Write the linear regression equation for the data in the chart Volume decimal places x Question Hel where x is the grams of the unknown metal Round your answers to 3 B If the mass of an unknown metal is 14 using your un rounded regression equation find its predicted volume Round your answer to 1 decimal place mL