Statistics Questions

16 An insurance company sells a one year term life insurance policy to a 70 year old man The man pays a premium of 400 If he dies within one year the company will pay 10 000 to his beneficiary The probability that a 70 year old man is still alive one year later is 0 9715 Let X be the profit made by the insurance company Find the expected value of the profit

19 In a recent Pew poll 10 of adults said that they consider themselves to be gamers Assume that 18 adults are randomly sampled a Compute the probability that exactly three of them consider themselves to be gamers b Find the probability that fewer than two of them consider themselves to be gamers c Find the probability that more than two of them consider themselves to be gamers

3 Decide if the following is a probability distribution X P x 1 0 25 2 0 65 3 0 30 4 0 11

Compute the least squares regression line for predicting selling price from size Selling Size Square Feet Price 1000s 400 2521 2555 2735 2846 3028 3049 3198 3198 426 428 435 469 475 488 455

17 Compute the mean and standard deviation of the following probability distribution using the TI 84 PLUS X P x 0 1 2 3 0 2 0 5 0 2 0 1

11 If 2 cards are selected from a standard deck of cards The first card is NOT placed back in the deck before the second card is drawn Find the following probabilities a P heart and club b P red card and a 4 of spades

14 Following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in 1 2 3 P x 0 06 0 14 0 45 0 21 0 14 X 0 4 a Find the probability that a student participates in exactly two activities b Find the probability that a student participates in more than two activities c Find the probability that a student participates in at least one activity

10 A bag contains 6 orange 8 blue and 4 yellow marbles What is the probability of selecting 2 blue marbles in succession providing the marble drawn first is then replaced before the second is drawn

8 A card is drawn from a standard deck of cards What is the probability of drawing an ace or a black card

9 Each of the numbers from 1 to 30 is written on a card and placed in a bag If one card is drawn at random what is the probability that the number is a multiple of 2 or a multiple of 3

a 1 For which of the following scatterplots is the correlation coefficient an appropriate summary b Food i c

5 Suppose a person buys a raffle ticket for 20 at a fundraising event 1000 tickets are sold and one winner is selected The winning ticket holder receives 5 000 Let the random variable X represent the possible profits for a ticket holder Construct a probability distribution for X

7 A card is selected from a deck of 52 cards What is the probability it is a red card or a Face card

6 Angel has 6 nickels 4 pennies and 3 dimes in her pocket She takes one coin from her pocket at random What is the probability if is a penny or a nickel

3 At the final exam in a statistics class the professor asks each student to indicate how many hours he or she studied for the exam After grading the exam the professor computes the least squares regression line for predicting the final exam score from the number of hours studied The equation of the line is 50 5x a Antoine studies for 6 hours What do you predict his exam score to be b Emma studied for 3 hours longer than Jeremy did How much higher do you predict Emma s score to be

o determine whether living near high voltage power lines is related to whether a person develops cancer researchers recrui ample of people and determined whether each one lived within 500 meters of high voltage power lines Subjects were follow 5 years to determine whether they developed cancer Cancer No Cancer Total Near Power Lines QUESTION 4 590 9258 9848 Not Near Power Lines 577 12535 13112 Total 1167 21793 22960 What is the alternative hypothesis to determine whether there is an association between living near power lin eveloping cancer P P OP P OP P p 0 5 OP P Which of the following p values gives the strongest evidence against the null hypothesis 0 009

Steel rods are manufactured with a mean length of 29 centimeter cm Because of variability in the manufacturing process the lengths of the rods are approximately normally distributed with a standard deviation of 0 08 cm Complete parts a to d a What proportion of rods has a length less than 28 9 cm 0 1056 Round to four decimal places as needed b Any rods that are shorter than 28 84 cm or longer than 29 16 cm are discarded What proportion of rods will be discarded 0 0455 Round to four decimal places as needed c Using the results of part b if 5000 rods are manufactured in a day how many should the plant manager expect to discard Use the answer from part b to find this answer Round to the nearest integer as needed

As a part of her studies Renee gathered data on the heights of 20 professional soccer players She works through the testing procedure Ho 75 H 75 a 0 04 The test statistic is to 2 445 The critical value is to 04 1 85 10 At the 4 significance level does the data provide sufficient evidence to conclude that the mean heights of soccer players is less than 75 inches Select the correct answer below We should reject the null hypothesis because to to So at the 4 significance level the data provide sufficient evidence to conclude that the average heights of soccer players is less than 75 inches We should not reject the null hypothesis because to to So at the 4 significance level the data do not provide sufficient evidence to conclude that the average heights of soccer players is less than 75 inches O We should reject the null hypothesis because to ta So at the 4 significance level the data provide sufficient evidence to conclude that the average heights of soccer players is less than 75 inches We should not reject the null hypothesis because to ta So at the 4 significance level the data do not provide sufficient evidence to conclude that the average heights of soccer players is less than 75 inches

Scenario 1 What is the probability that a marble randomly pulled from a bag is yellow OR red Click here for diagram answer In this scenario OR means we are looking for the items in union Therefore P red OR yellow P R UY fraction bar the two circles which is the Enter your answer as a reduced fraction using for th

Simple Event B G R Y Outcome of Interest Choose a marble that is not green Choose a marble that is not red Choose a marble that is not blue Choose a marble that is not yellow where az is the probability of choosing the color 1 3 10 1 1 15 2 5 10 P x where z is the simple event P G 7 10 P R 3 P B P Y 14 15 10

A person with high emotional intelligence has The ability to be aware of and manage their own emotions as well as their social interactions A high level of knowledge about emotions A high level of intelligence The ability to not feel their emotions and to help others be calm

An off capus student wants to know whether it is faster to walk or take the bus to campus For 6 weeks the student flips a coin ea morning to decide whether to walk or take the bus Each day they record how they got to campus and how many minutes it took to get there What is the parameter of interest Difference in means Difference in proportions Correlation Single mean Single proportion

To determine whether living near high voltage power lines is related to whether a person develops cancer researchers recruited a sample of people and determined whether each one lived within 500 meters of high voltage power lines Subjects were followed for 15 years to determine whether they developed cancer Total Cancer No Cancer Total 590 9848 590 22960 590 1167 590 9848 Which proportions would be compared to determine whether there is an association between living near power lines and developing cancer 9258 9848 and Cancer Total and and Near Power Lines 590 and No Cancer 9258 9848 O P P OP P OP P Q 577 22960 577 QUESTION 2 To determine whether living near high voltage power lines is related to whether a person develops cancer researchers recruited a sample of people and determined whether each one lived within 500 meters of high voltage power lines Subjects were followed for 15 years to determine whether they developed cancer Total 1167 577 13112 Not Near Power Lines 577 12535 13112 Near Power Lines 590 9258 9848 1167 21793 22960 Not Near Power Lines 577 12535 13112 1167 21793 22960 What is the null hypothesis to determine whether there is an association between living near power lines and developing cancer

A random sample of U S adults had both their armspan and their height measured in centimeters For each person the difference was calculated as follows difference armspan height A 95 confidence interval for the difference was calculated to be 6 1 3 5 Which of the following is true We can be 95 confident that for the people in the sample the mean armspan is between 3 5 and 6 1 centimeters less than the mean height 95 of U S adults have armspans between 3 5 and 6 1 centimeters less than their height On average people s heights are less than their armspans In the population of all U S adults we can be 95 confident that on average a person s armspan is between 3 5 and 6 1 centimeters less than their height

What is the null hypothesis to determine how strong the evidence is that on average U S adults take fewer than 7 000 steps per day On average U S adults take fewer than 7 000 steps per day On average U S adults take 7 000 steps per day On average U S adults take more than 5863 steps per day On average U S adults take 5863 steps per day QUESTION 6 A random sample of 2000 U S adults were given pedometers to determine how many steps they take per day Among the people in the sample the average number of steps per day was 5863 with standard deviation 2870 What is the alternative hypothesis to determine how strong the evidence is that on average U S adults take fewer than 7 000 steps per day On average U S adults take fewer than 7 000 steps per day On average U S adults take 7 000 steps per day On average U S adults take more than 5863 steps per day On average U S adults take 5863 steps per day

by dre years claim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of a 0 01 Which the awards were won Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to support a Click the icon to view the ages of the award winners Construct a scatterplot Choose the correct graph below A 70 10 20 20 70 Best Actress years Q The linear correlation coefficient is r 0 199 Round to three decimal places as needed Determine the null and alternative hypotheses Ho P H P 0 Type integers or decimals Do not round The test statistic is t 0 64 Round to two decimal places as needed The P value is 0 535 Round to three decimal places as needed Because the P value of the linear correlation coefficient is OB Best Actor yeam 70 20 n KT 14 20 70 Best Actress years Best Actresses and Best Actors Best Actress 29 29 Best Actor 42 37 Q Q less than or equal to Print the significance level there Done C Best Actor years 28 63 33 34 46 29 62 22 42 55 49 47 59 47 40 47 41 56 44 32 20 20 70 Best Actress years ww X Q Q 50 70 191 Holst 7 HERENT 200 BEHEER 201 20 70 Best Actress years 200 sufficient evidence to support the claim that there is a linear correlation between the ages of Best Actresses and Best Actors

A survey of 1 006 randomly selected adults living in London found that 584 of them had driver s licer What is the parameter of interest Difference in means Difference in proportions Correlation Single mean

SELECT ALL of the following that could be valid testable hypotheses H p 0 5 Hp 0 5 1 P 0 5 p H p 0 7 H OH P 0 5 H p 0 5 OHP 0 5 H p 0 5 HP p HP P

Find the z score such that the area under the standard normal curve to the left is 0 69 is the z score such that the area under the curve to the left is 0 69 Round to two decimal places as needed

c Find the area under the normal curve to the left of z 0 23 plus the area under the normal curve to the right of z 1 The combined area is Round to four decimal places as needed

Number of Calls Millions 16 14 12 10 00 O 4 Total 2 0 4 3 Nature of Call Complaint Product Purchase Payment North America Miscellaneous 4 0 Customer Service Calls Origin of Call by Region 14 1 14 8 2 1 2 4 Last Year This Year Asia Pacific 3 5 3 5 Europe Other Last Year Millions This Year Millions 8 0 8 0 6 9 6 0 3 1 24 0 7 0 7 0 2 7 24 7 2 What percentage of all customer service calls last year were regarding payment 25 26 27 28 29

Scores on a test are normally distributed with a mean of 76 and a standard deviation of 6 Using the z score table estimate the probability a randomly selected student scored below a 64 Select one a 0 98 Ob 1 2 c 0 02 d 0 02

Use the given shaded area 0 7035 in the middle of the standard normal distribution and the given z score 1 2 to find the missing z score The shaded region is not symmetric about z 0 Round your final answer to two decimal places 4 Shaded Area 0 7035 3 2 1 1 2 Upper z score 0 2 3 4 a

A small warehouse employs these full time positions approximately 40 hours a week a supervisor at 1200 a week an inventory manager at 700 a week six stock boys at 450 a week and four drivers at 500 a week employees earn more than the mean wage

Using the standard normal distribution find the two z scores that that form the middle shaded region The shaded region is symmetric about z 0 Round your z scores to two decimal places Shaded Area 0 64 Negative z score Positive z score 112 2 3 4 a

Consider the Lagrange polynomial p x 5 10 x 15 1 x 2 l x corresponding the table Y What is the value of 1 x at x 6 3 5 15 8 2

a b c d e 4 Which one of the following is the highest order Lagrange polynomial of the data below x 3x 1 2x 3x 1 2x 3x 1 3x 1 2x 3x X y 0 1 1 0 2 3

accompanying table lists the ages of acting award winners matched by the years in which the awards were won Construct a scatterplot find the value of the linear correlation coefficient r and find the P value of r Determine whether there is sufficient evidence to suppor claim of linear correlation between the two variables Should we expect that there would be a correlation Use a significance level of a 0 01 Click the icon to view the ages of the award winners Construct a scatterplot Choose the correct graph below OA 70 20 20 70 Best Actress years Q Q 2 The linear correlation coefficient is r 0 199 Round to three decimal places as needed Determine the null and alternative hypotheses Ho P 0 H P 0 Type integers or decimals Do not round The test statistic is t 0 64 Round to two decimal places as needed The P value is Round to three decimal places as needed OB Best Actor yeam 70 20 20 70 Best Actress years Q Q Best Actress 29 29 Best Actor 42 37 5 Best Actresses and Best Actors 28 63 33 34 46 29 40 47 49 47 59 47 Print Done 62 41 GILB C 22 56 44 44 Best Actor yeam 20 20 70 Best Actress years 42 55 32 X Q Q 5 OD 70 4 Te 20 20 70 Best Actress years Q Q G

esearchers conducted a study to determine whether magnets are effective in treating back pain Pain was easured using the visual analog scale and the results shown below are among the results obtained in the study igher scores correspond to greater pain levels Assume that the two samples are independent simple random amples selected from normally distributed populations and do not assume that the population standard deviations re equal Complete parts a to c below Reduction in Pain Level After Magnet Treatment n 30 x 0 45 s 0 92 Reduction in Pain Level After Sham Treatment n 30 x 0 35 s 1 51 H H1 H OC Ho 2 H H H H1 H1 H2 D Ho P P2 H H P The test statistic t is 0 31 Round to two decimal places as needed The P value is 0 379 Round to three decimal places as needed State the conclusion for the test Fail to reject the null hypothesis There is not sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment b Construct a confidence interval appropriate for the hypothesis test in part a 04 2 0

below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million e for different countries Construct a scatterplot find the value of the linear correlation coefficient r and find value of r Determine whether there is sufficient evidence to support a claim of linear correlation between the ariables Use a significance level of 0 01 ternet Users ward Winners 30 Internet Users 90 80 2 80 8 57 0 5 4 9 2 3 3 5 0 30 Internet Users inear correlation coefficient is r 0 820 nd to three decimal places as needed rmine the null and alternative hypotheses D 0 D 0 e integers or decimals Do not round P value is ind to thron donimel mi test statistic is t 2 87 und to two decimal places as needed 90 67 2 1 6 G 79 5 10 4 0 30 38 7 0 1 La Internet Users 90 0 30 Internet Users 90 G

A study was done using a treatment group and a placebo group The results are shown in the table Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b below Use a 0 05 significance level for both parts a Test the claim that the two samples are from populations with the same mean What are the null and alternative hypotheses OA Ho Hy 2 H H H OC Ho H H H H H The test statistic t is 1 90 Round to two decimal places as needed The P value is 0 063 Round to three decimal places as needed State the conclusion for the test GELED b Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean 14 27 4 B Ho H H H H H OD Ho H H H H1 H A Fail to reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean OB Reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean C Reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean D Fail to reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean 3CX Treatment Place H 35 2 31 0 94 TON H 37 2 66 0 57

Male BMI H Given in the table are the BMI statistics for random samples of men and women Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b below Use a 0 01 significance level for both parts n 40 X 28 3394 S 7 959978 G The test statistic t is 2 14 Round to two decimal places as needed The P value is 0 032 Round to three decimal places as needed State the conclusion for the test Female BMI H 40 25 2003 4 804346 O A Reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI OB Reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI C Fail to reject the null hypothesis There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI OD Fail to reject the null hypothesis There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI b Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI 014 12 0

Find the percentage of the total area under the standard normal curve between the following 2 scores z 2 48 and z 0 05 Click here for page 1 of the Areas under the Normal Curve Table Click here for page 2 of the Areas under the Normal Curve Table The percentage of the total area between 2 2 48 and z 0 05 is Round to two decimal places as needed Areas under the Normal Curve page 1 Areas under the Normal Curve The column under A gives the proportion of the area under the entire curve that is between z 0 and a positive value of z z A A z 3315 1 44 3340 1 45 2 1844 96 1879 97 1915 1950 99 3389 1 47 1985 1 00 3413 1 48 2019 1 01 3438 1 49 98 3365 1 46 4306 4319 4332 4345 1 04 3508 1 52 4382 2054 1 02 3461 1 50 2088 1 03 3485 1 51 2123 4357 2157 1 05 3631 1 53 4370 2190 1 06 3554 1 54 2224 1 07 3577 1 55 2258 1 08 3599 1 56 2291 1 09 3621 1 57 2324 1 10 3643 1 58 2357 1 11 3665 1 59 2389 1 12 3686 1 60 4394 4406 4418 4430 Com Z 00 01 02 03 04 0160 05 0199 06 0239 0279 07 08 0319 0359 0398 0438 0478 13 0517 0557 0596 0636 BETE 888 SIN688 09 10 11 12 14 15 A 0000 0040 0080 0120 51 16 IT 2988283886 48 49 50 52 53 54 55 56 57 58 59 60 28828 61 62 63 64 A 4251 4265 4279 4292 4441 4452 PORN

A basketball team sells tickets that cost 10 20 or for VIP seats 30 The team has sold 3207 ticke tickets of each kind have been sold How many 10 tickets were sold How many 20 tickets were sold tickets overall It has How many 30 tickets were sold thas sold 127 more 20 tickets than 10 tickets The total sales and 50 540 How many CHO

The probability distribution of the egg production of a farmer s chickens is given below What is the expected egg production for any one chicken Round to the nearest tenth n eggs Probability of n eggs 3 0 25 3 4 eggs per chicken are expected 3 8 eggs per chicken are expected 3 6 eggs per chicken are expected 4 0 eggs per chicken are expected 4 0 7 5 0 05

According to a report 61 2 of murders are committed with a firearm a If 100 murders are randomly selected how many would we expect to be committed with a firearm b Would it be unusual to observe 77 murders by firearm in a random sample of 100 murders Why a We would expect to be committed with a firearm b Choose the correct answer below A Yes because 77 is between 2o and 20 OB No because 77 is greater than 20 OC Yes because 77 is greater than 20 OD No because 77 is between 20 and 20 E No because 77 is less than 20 www

According to flightstats com American Airlines flights from Dallas to Chicago are on time 80 of the time Suppose 10 flights are randomly selected and the number of on time a Explain why this is a binomial experiment b Determine the values of n and p c Find and interpret the probability that exactly 6 flights are on time d Find and interpret the probability that fewer than 6 flights are on time e Find and interpret the probability that at least 6 flights are on time f Find and interpret the probability that between 4 and 6 flights inclusive are on time c Using the binomial distribution the probability that exactly 6 flights are on time is Round to four decimal places as needed Interpret the probability In 100 trials of this experiment it is expected that about will result in exactly 6 flights being on time Round to the nearest whole number as needed d Using the binomial distribution the probability that fewer than 6 flights are on time is Round to four decimal places as needed Interpret the probability In 100 trials of this experiment it is expected that about Round to the nearest whole number as needed will result in fewer than 6 flights being on time e Using the binomial distribution the probability that at least 6 flights are on time is Round to four decimal places as needed Interpret the probability In 100 trials of this experiment it is expected that about Round to the nearest whole number as needed will result in at least 6 flights being on time f Using the binomial distribution the probability that between 4 and 6 flights inclusive are on time is Round to four decimal places as needed Interpret the probability D inclusivo being on time

a healthy diet on depression levels the resea the experiment and then again three weeks later The response variable is the reduction in BMI so larger numbers indicate greater reduction Test whether these experimental results allow us to conclude that on average change in BMI is higher for those who eat a healthy diet for three weeks than for those who don t The data is available on StatKey and in Diet Depression Let Group 1 represent those with a healthy diet and Group 2 represent those with no diet change 4 Give notation of the sample statistic Sample statistic eTextbook and Media H i 0 001 21 1 x2 p X Your answer is incorrect Try again 42 Give value of the sample statistic accurate to three decimal places A P1 p A P2 S S P1 T P2 H p HI Use a randomization distribution to find the p value Give your answer accurate to three decimal places Edit

This question 1 point s possible In a poll 1 002 men in a country were asked whether they favor or oppose the use of federal tax dollars to fund medical research using stem cells obtained from human embryos Among the respondents said that they were in favor Identify the population and the sample What is the population in the given problem Choose the correct answer below OA 48 of the 1 002 men selected OB The 1 002 men selected OC 48 of all men in the country OD All men in the country Identify the sample for the given problem Choose the correct answer below A The 1 002 men selected OB 48 of the 1 002 men selected OC All men in the country OD 48 of all men in the country Submit qu

K A pharmaceutical company wants to test the effectiveness of a new allergy drug The company identifies 250 females 30 35 years old who suffer from severe allergies The subjects are randomly assigned into two groups One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug After six months the subjects symptoms are studied and compared Answer parts a through c below CB a Identify the experimental units and treatments used in this experiment Choose the correct answer below OA The experimental unit is the new allergy drug The treatments are the severe allergies the patients suffer from OB The experimental units are the 30 to 35 year old females being given the treatment The treatment is the new allergy drug OC The experimental units are the symptoms from the drug The treatment is the new allergy drug OD The experimental units are the 30 to 35 year old females being given the treatment The treatment is six months b Identify a potential problem with the experiment design being used and suggest a way to improve it Choose the correct answer below OA There are no biases present OB There may be a bias on part of the experiment since only females are being tested OC There may be a bias on the part of the patients since they do not know if they were given the placebo or the real drug OD There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug c How could this experiment be designed to be a double blind Choose the correct answer below OA The study would be a double blind study if the patient knew if they received the real drug or the placebo but the researcher did not OB The study would be a double blind study if all patients received the placebo and no patient received the real drug OC The study would be a double blind study if both the researcher and the patient did not know which patient received the real drug or the placebo OD The study would be a double blind study if both the researcher and the patient knew if they received the real drug or the placebo