Statistics Questions and Answers

Growth spurt It is generally known that boys grow at an unusually fast rate between the ages of about 12 and 14 Following are heights in inches of 10 b neasured at age 12 and again at age 14 Can you conclude that the mean increase in height is greater than 5 inches Let represent the mean height at a 4 and Use the a 0 10 level and the P value method with the TI 84 Plus calculator Age 12 Age 14 Part 0 4 Send data to Excel Part 1 of 4 H Height 61 4 60 7 55 9 59 7 56 3 63 0 58 6 61 1 59 5 61 6 67 0 65 5 62 1 65 4 61 5 68 5 63 9 65 8 64 5 66 3 a State the appropriate null and alternate hypotheses Ho 0 0 0 Ha

Vegan Thanksgiving Tofurkey is a vegan turkey substitute usually made from tofu At a certain restaurant the number of calories in a serving of tofurkey with wild mushroom stuffing and gravy is normally distributed with mean 486 and standard deviation 24 Part 0 2 Part 1 of 2 a What proportion of servings have between 494 and 510 calories Round the answer to four decimal places The proportion of servings that have between 494 and 510 calories is

18 Brown tree snakes are an invasive species causing huge environmental and financial damage in Guam Researchers captured 504 brown tree snakes on Guam s Andersen Air Force Base The distribution of brown tree snake weights was clearly right skewed On average the snakes weighed 121 g standard error of the mean SEM 3 g and ranged from 23 to 663 g at capture What is a 95 confidence interval for the mean weight of brown tree snakes in Guam approximately Show work 23 0 to 663 0 g 115 1 to 126 9 g a b c 118 0 to 124 0 g d 120 7 to 121 3 g

20 Post exposure radiation levels are approximately Normally distributed with mean The levels in Sv of a random sample of three trauma victims who were recently exposed are 5 5 6 2 and 4 8 Sv What is a 95 confidence interval for u based on these data hint s 0 7

24 A 95 confidence interval for the mean lead concentration in the urine of adult men working with lead for smelting is 8 22 to 11 98 micrograms per liter g l The numerical value of the margin of error for this confidence interval is 118 1

23 A 95 confidence interval for u is a wider than b narrower than C exactly the same as d not significantly different from the 99 confidence interval for u

17 The height in inches of males in the United States is believed to be Normally distributed The average height of a random sample of 50 American adult males is 69 72 inches and the standard deviation of the 50 heights is s 4 23 What is the standard error of X

15 A medical researcher treats 100 subjects with high cholesterol levels with a new drug The average decrease in cholesterol level is 80 after two months of taking the drug Assume that the decrease in cholesterol after two months of taking the drug follows a Normal distribution with unknown mean u and standard deviation 20 What is the 90 confidence interval for u based on these data

11 The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9 8 kg and standard deviation 0 1 kg If you take a random sample of 25 adult men with liver cirrhosis what is the probability that their average total body protein is between 9 75 and 9 85 kg

0 0 15 1 0 15 2 0 2 3 0 5 Find the standard deviation of this probability distribution Use your mean rounded to 2 decimal plac Give your answer to 2 decimal places

W The average resting heart rate of a population is 87 beats per minute with a standard deviation of 10 bpm Find the z scores that correspond to each of the following heart rates Round your answers to the nearest hundredth if necessary a 97 bpm Z b 80 bpm Z

For a standard normal distribution find P 0 92 z 2 26

he following MINITAB output display presents a 98 confidence interval for the difference between two means A B N 17 25 Part 1 of 3 SE Mean 72 9172 10 7134 2 5984 Part 0 3 Mean StDev Difference mu A mu B 52 1743 9 1237 1 8247 Estimate for difference 20 7429 98 CI for difference 12 9408 28 5450 DF 30

Water loss Human skin loses water through evaporation and in general damaged skin loses water at a faster rate than undamaged skin In a study in which the outer layer of skin on a small section of the forearm was partially removed water loss in g m per hour was measured both before and after skin removal The results for ten individuals were as follows Subject 1 2 3 4 5 6 7 8 9 10 Part 0 2 Before After 16 25 11 18 15 27 14 22 26 21 28 27 21 28 Send data to Excel Part 1 of 2 16 13 11 18 11 15 a Construct a 90 confidence interval for the mean increase in water loss Let d represent the water loss after skin removal minus the water loss before skin removal in g m per hour Use the TI 84 Plus calculator and round the answers to one decimal place 90 confidence interval for the mean increase in water loss is

Els Testing Test The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0 4 parts per million ppm A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer The levels in ppm are shown below 0 31 0 47 0 19 0 72 0 56 0 91 0 29 0 83 0 49 0 28 0 31 0 46 0 25 0 34 0 17 0 58 0 19 0 26 0 47 0 81 Does the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0 4 ppm Use a 0 05 significance level to test the claim that these sample levels come from a population with a mean greater than 0 4 ppm Use the P value method of testing hypotheses Assume that the standard deviation of levels of the chemical in all such tomatoes is 0 21 ppm Choose the correct test statistic and P value associated with this experiment Test statistic z 0 95 P value 0 1711 Test statistic z 0 95 P value 0 1711

8 Complete the table below for options for diversification of the investments assume all money is invested and the goal of 10 return is satisfied Write not possible in the box if it is not possible to satisfy the investment goals with the given allocation Account A 0 200 000 Account B 200 000 Account C 0 150 000 9 What is the maximum amount that could be invested in account C while still investing all of the available money and satisfying the given goal of 10 overall interest What is the minimum amount that must be invested in account C to achieve the desired goal

A bag contains 10 yellow marbles 3 green marbles 7 blue marbles If one marble is drawn from the bag then replaced what is the probability of drawing a yellow marble then a blue marble In a number guessing game You ask a person to guess a number from one 1 to 10 If the person makes a random guess what is the probability their guess will be less than 8 A bag contains 3 white marbles 7 blue marbles 10 green marbles If one marble is drawn from the bag but not replaced what is the probability of drawing a white marble then a green marble

A marketing research company is estimating which of two soft drinks college students prefer A random sample of n college students produced the following 99 confidence interval for the proportion of college students who prefer drink A 0 232 0 592 Identify the point estimate for estimating the true proportion of college students who prefer that drink O 0 592 O 0 5 O 0 232 O 0 412 O 0 18

9 An engineer at General Motors collects data on the weights in pounds and the fuel economy in miles per galle of all model year 2000 cars sold by GM We expect the correlation between weight and gas mileage to be a clearly positive b close to zero c clearly negative d can t tell because correlation is random el can t tell because correlation

In deciding whether the ANOVA test can be used you check whether the largest group standard deviation is no more than twice the smallest group standard deviation But your printout contains only variance Knowing that the Standard Deviation is just the square root of variance decide whether the largest group standard deviation is no more than twice the smallest group standard deviation given Largest Group Variance is 61 54 and Smallest Group Variance is 34 88 Select the best answer 61 54 O Because 2 it is reasonable to assume that the populations all have the same standard deviation 34 88 O Because 61 54 34 88 deviation O Because 61 54 2 it is reasonable to assume that the populations do not all have the same standard 34 88 deviation 61 54 34 88 2 it is reasonable to assume that the populations all have the same standard Because deviation 2 it is reasonable to assume that the populations do not all have the same standard

Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest The following data give the call to shock time in minutes and the survival percentage rate of patients at a cardiac rehabilitation center Time minutes Survival rate 2 90 3 70 5 55 6 45 7 30 5 Make a scatterplot of the data by hand Make sure to label the axes use nice appropriate scaling 8 8 6 Explain in simple language what this plot says about the two variables 9 5 11 4

In Lab 4 you also analyzed the cell phone use of students several years back At that time it was known that about 80 of all college students owned a cell phone In your analysis you found that a 95 confidence interval for the percentage of students in this university who owned a cell phone was 0 74 0 83 You also tested whether the data provide evidence that the proportion of students who own cell phones in this university is lower than the national figure You found the p value for that test was 0 24 Which of the following statements follow from this analysis Mark all that apply We are 95 confident that the proportion of students at this college who own a cell phone is between 0 74 and 0 83 Since 0 80 is in this interval we have inadequate evidence to conclude that the proportion of students at this university who own a cell phone is less than the national figure We are 95 confident that the proportion of students at this college who own a cell phone is between 0 74 and 0 83 Since 0 80 is in this interval we have enough evidence to conclude that the proportion of students at this university who own a cell phone is less than the national figure Since our p value is greater than our level of significance we conclude that our data is not adequate to conclude that the proportion of students at this college who own a cell phone is lower than the national figure Since 78 of the students sampled owned a cell phone we know that the percent of students at this school who own a cell phone is less than 80 the national figure

Satisfied A 2010 poll asked people in the United States whether they were satisfied with their financial situation A total of 298 out of 1157 people said they were satisfied The same question was asked in 2012 and 343 out of 828 people said they were satisfied Part 0 2 Part 1 of 2 a Construct a 95 confidence interval for the difference between the proportions of adults who said they were satisfied in 2012 and 2010 Let p denote the proportion of individuals satisfied with their financial situation in 2012 and p denote the proportion of individuals satisfied with their financial situation in 2010 Round the answers to three decimal places 05 confidence intorul for th difference between fndulto who coid ntinfind in 2012 and 2010

Identify the sampling technique used At a local community college five statistics classes are randomly selected out of 20 and all of the students from each class are interviewed stratified convenience O cluster systematic random

Identify the sampling technique used A community college student interviews everyone in a statistics class to determine the percentage of students that own a car systematic random cluster convenience stratified

Use the grouped data formulas to find the indicated mean or standard deviation The speeds of a random sample of 100 cars are recorded as they pass a highway checkpoint The results are summarized in the frequency distribution below Approximate the sample mean Speed mph Cars 30 39 6 40 49 15 50 59 51 60 69 15 70 79 13 O 55 9 mph 58 7 mph O 54 5 mph 61 5 mph

Provide an appropriate response A group of students were asked if they carry a credit card The responses are listed in the table Class Freshman Sophomore Total O 0 584 0 250 If a student is selected at random find the probability that he or she owns a credit card given that the student is a freshman Round your answer to three decimal places O 0 750 Credit Card Not a Credit Card Carrier 15 8 23 O 0 450 Carrier 45 32 77 Total 60 40 100

Provide an appropriate response For the mathematics part of the SAT the mean is 514 with a standard deviation of 113 and for the mathematics part of the ACT the mean is 20 6 with a standard deviation of 5 1 Bob scores a 660 on the SAT and a 27 on the ACT Use z scores to determine on which test he performed better

Identify whether the statement describes inferential statistics or descriptive statistics From past figures it is predicted that 19 of the registered voters in California will vote in the June primary descriptive statistics

Provide an appropriate response The mean score of a competency test is 77 with a standard deviation of 4 Use the Empirical Rule to find the percentage of scores between 69 and 85 Assume the data set has a bell shaped distribution 95 50

D Question 31 Provide an appropriate response Decide if the events A and B are mutually exclusive or not mutually exclusive A die is rolled A The result is an odd number B The result is an even number not mutually exclusive 2 5 pts

Provide an appropriate response The heights in inches of 10 adult males are listed below Find the sample standard deviation of the data set 70 72 71 70 69 73 69 68 70 71 O 2 38 O 70 O 3 O 1 49

Identify the data set s level of measurement list of zip codes for Chicago O nominal O interval Oratio ordinal

Provide an appropriate response Find the sample standard deviation 15 42 53 7 9 12 14 28 47 O 29 1 15 8 O 16 6 O 17 8

Provide an appropriate response Given that P A or B 1 P A O 71 252 O 252 252 and P A and B find P B

Identify the sampling technique used Based on 12 500 responses from 48 000 questionnaires sent to its alumni a major university estimated that the annual salary of its alumni was 78 500 per year random convenience stratified O cluster O systematic

Provide an appropriate response 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 employees to program and 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 72 and 5 respectively and the distribution of scores is bell shaped and symmetric Suppose the trainee in question received a score of 68 Compute the trainee s z score O z 0 80 O z 0 8 O z 0 88 OZ 0 88 5

Determine whether the data are qualitative or quantitative the number of seats in a movie theater A qualitative O quantitative

Provide an appropriate response 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 shaped distribution 99 7 100 O 68 95

Provide an appropriate response 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 mean score in the class O 80 6 O 76 6 O 90 6 O 85 6

The following information pertains to the Flying Fig Corporation Total Units for information given Fixed Cost per Unit Selling Price per Unit Variable Costs per Unit Target Operating Income What is the breakeven in sales dollars Round any intermediary calculations and your final answer to the nearest whole numb OA 844 444 B 422 222 OC 380 000 OD 422 275 4 000 50 475 250 200 000

Provide an appropriate response In a pizza takeout restaurant the following probability distribution was obtained The random variable x represents the number of toppings for a large pizza Find the mean and standard deviation x P x 0 0 30 1 0 40 2 0 20 3 0 06 4 0 04 mean 1 54 standard deviation 1 30 mean 1 14 standard deviation 1 04 mean 1 30 standard deviation 1 54 mean 1 30 standard deviation 2 38

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p n 7 p 0 9 P Fewer than 4 O 0 9973 O 0 0257 0 0027 O 0 0002

Question 4 Identify the data set s level of measurement temperatures of 12 selected refrigerators nominal ordinal O ratio O interval 2 5

Question 3 Determine whether the data are qualitative or quantitative the colors of automobiles on a used car lot quantitative

Question 2 Provide an appropriate response State whether the variable is discrete or continuous The temperature in degrees Fahrenheit on July 4th in Juneau Alaska discrete continuous

Homework Onlapter 7 Homework Question list K Oleg s Steel Parts produces parts for the

Kurre has the following utility function U x z x 0 33 70 67 where x the quantity consumed of good x and z the quantity consumed of good z The unit price of good x is Px and the unit price of good z is Pz Kurre s income is Y Define MRS and MRT and use those concepts to show how you get to a Kurre s demand function for good x and b Kurre s demand function for good z du MRS MRT f du 2Z b 67x 67 33 Z 2 67 38

a First Determine how many significant figures are in each of the figures a 1 898 000 000 000 tons has significant digits b 2000 Lbs has significant digits C 2 5 has significant digits b Convert each Value in Scientific notation if possible Significant digits times 10 raised to some power then add in units a b C ons to Couric with your final answer with the

Exam Score 86888 0 r 0 72 10 Number of Missed Classes above scatterplot represents the number of absences sed classes that a class period of students had and their es on a semester exam The correlation strength of the data could be described as 21 The correlation with exam score for missing more than 15 classes is Select than it is for missiog less than 15 22 There is Select In the semester and their exam score between the number of classes a student i