Probability Questions and Answers

Curing diabetes Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss In a recent study 82 patients with Type 2 diabetes underwent this procedure and 59 of them experienced a recovery from diabetes Does this study provide convincing evidence that those with diabetes who undergo this surgery will recover from diabetes differs from 56 Use the a 0 01 level of significance with the P value method and Excel Part 0 5 Part 1 of 5 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 5 07 P X 8 0 B DI V d

Part 0 5 LA Game consoles A poll surveyed 341 video gamers and 81 of them said that they prefer playing games on a console rather than a computer or hand held device An executive at a game console manufacturing company claims that less than 27 of gamers prefer consoles Does the poll provide convincing evidence that the claim is true Use the a 0 01 level of significance with the P value method and Excel Part 1 of 5 5 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 0 0 O O 0 0 p X 0 0

Find the standardized test statistic t for the hypothesis test defined by H 13 6 z 13 2 8 2 0 n 20 and a 0 05 Round your answer to three decilmall places 0894 1 233 0 872

Construct a 95 confidence intervall for the popallation mean Assume the population has a normal distribution A sample of 20 part time workers had mean annual earnings of 3120 with a standard deviation of 677 Round to the neare 2803 3437 2135 2567 2657 2891 1324 1567

Find the indicated probability Assume that the random variable Xs normally didt buted with mean p standard deviation 16 Compute the probability PX90 CO POSS

In a recent survey 67 of the community favored building a health center in the neighborhood If 14 citizens are chosen find the probability that exactly 9 of th favor the building of the health center 0670 0085

At a particular point in time the stock marken ook big wings up and down A survey of 999 adult investors and how often thang bracked their portfolio The table shows the investor responses What is the probability that an adult investor tracks his or her portfolio daily Express your answer as a simplified fraction and as a decimall rounded to three decimal places

transcript Brianna is buying a house for 220 000 She plans to make a 18 down payment Closing costs include 700 for 6 months of homeowners insurance 600 for 6 months of property tax 125 for the title fee and 350 in transaction fees Brianna also agreed to pay four points in exchange for a 1 reduction in interest rate Determine the amount of money Brianna needs to cover closing costs Round your answer to the nearest cent Answer 2 Points Key Keyboard Sho

the close of the stock markets on a day in 2017 there were 6100 companies listed with certain stock exchanges On this day the probabilities of advancing eclining and unchanged company stocks appears in the table for the two exchanges Find the probability that a stock was listed on Exchange 2 given that it dvanced Exchange Exchange 1 Exchange 2 Percentage of Probability of Probability of Stock Stock Companies Listed 0 5209 Advancing Declining 0 7224 0 2492 0 4791 0 6224 0 3255 Let F be Exchange 2 and E be an advance R E and P F Probability the Stocks Remain Unchanged 0 0284 0 0521

Provide an appropriate response Which branch of statistics deals with the organization and summarization of collected information Inferential statistics Computational statistics Descriptive statistics

34 Hy p They find that p value 00025 and use an a 001 level of significance Do the environmental engineers have enough evidence to say the level of lead in the water is significantly higher than the standard Since the p value there is insufficient evidence that the level of lead is significantly higher than the standard theire is sufficient evidence that the level of lead is Since the p value significardly higher than the standard Since the p value significantly higher than the standard there is insufficient evidence that the level of lead is Since the p value o there is sufficient evidence that the level of head is significantly higher than the standard

d Determine whether to reject Ho Reject Part 4 5 Part 5 of 5 the null hypothesis Ho e State a conclusion There Choose one enough evidence to conclude that the mean commute time is greater than 25 minutes

Ticon one way commute time was 20 minutes with a standard deviation or 15 minutes A transportation engineer Ciams that the meort commote time is greater than 25 minutes Do the data provide convincing evidence that the engineer s claim is true Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator Part 1 of 5 a State the appropriate null and alternate hypotheses Hoi 25 H 25 This hypothesis test is a right tailed Y test Part 1 5 Part 2 of 5 b Compute the value of the test statistic Round the answer to two decimal places Ella Espe OF B 42 P dlo E

Part 0 5 Part 1 of 5 2 3 Ho H 4 Is there a doctor in the house A market research firm reported the mean annual earnings of all family practitioners in the United States was 178 258 A random sample of 44 family practitioners in Los Angeles had mean earnings of x 193 250 with a standard deviation of 41 407 Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles differs from the national average Use the a 0 01 level of significance and the P value method with the TI 84 Plus calculator 5 a State the appropriate null and alternate hypotheses This hypothesis test is a Choose one Y test O O 6 X 00 7 0 0 0 co 7 Hel 40 M d

A 2011 Gallup survey based on telephone and face to face interviews with 4 220 adults in China aged 15 and older suggests that 30 smoke regularly or occasionally The following is also noted one can say with 95 confidence that the maximum margin of sampling error is 2 1 percentage points Which of the following is true based on the results of this survey OWe are 95 confident that 27 9 to 32 1 of all Chinese adults smoke O Exactly 30 of all Chinese adults smoke Olf we were to randomly sample another group of 4 220 Chinese adults we would find that exactly 30 of them smoke as well We are 95 confident that 25 8 to 34 2 of all Chinese adults smoke If the sample size was larger the margin of error would be larger as well

Find the sum of squares error E for the least squares line fit to the four points in the figure Q AY y 11x43 8 6 odu G E Type an integer or a decis

Trydint bubble gum company claims that 8 out of 10 people prefer their gum to Eklypse Test their claim at the 90 confidence level The null and alternative hypothesis in symbols would be Ho 20 8 H 0 8 Ho p20 8 H p 0 8 Ho p 0 8 H 0 8 Ho p 0 8 H p 0 8 Ho p 0 8 H p 0 8 Ho 0 8 H 0 8 The null hypothesis in words would be The proportion of all people that prefer Trydint gum is less than 0 8 The proportion of people in a sample that prefer Trydint gum is not 0 8 The proportion of all people that prefer Trydint gum is greater than 0 8 The average of people that prefer Trydint gum is 0 8 The average of people that prefer Trydint gum is not 0 8 The proportion of all people that prefer Trydint gum is 0 8 The proportion of people in a sample that prefers Trydint gum is 0 8

a State the appropriate null and alternate hypotheses b Compute the P value c State a conclusion Use the a 0 01 level of significance Part 1 of 4 a State the appropriate null and alternate hypotheses Ho 20 8 H 20 8 This hypothesis test is a two tailed Part 1 4 Part 2 of 4 test b Compute the P value Round the answer to at least four decimal places

sample of 180 six year old girls weighed between 2003 and 2006 had an average weight of 50 4 pounds Assume the population standard deviation is a 16 5 pounds Can you conclude that the mean weight of six year old girls is higher in 2006 than in 2002 Use the a 0 10 level of significance and the P value method with the TI 84 calculator Part 1 of 4 State the appropriate null and alternate hypotheses Ho 49 3 H 49 3 The hypothesis test is a right tailed Part 1 4 Part 2 of 4 test Compute the P value Round your answer to at least four decimal places Espa o C E 5 d

Lifetimes of AAA batteries are approximately normally distributed A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces A random sample of 16 AAA batteries produced by this manufacturer lasted a mean of 11 hours with a standard deviation of 1 8 hours Find a 90 confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer Then give its lower limit and upper limit Carry your intermediate computations to at least three decimal places Round your answers to at least two decimal places If necessary consult a list of formulas Lower limit Upper limit X

What are the degrees of tre d f 4 What is the critical value for this sample Round to four decimal places critical value 13 277 Complete the table by calculating the expected frequencies Observed Expected Category Frequency Frequency A B C D E 14 13 13 5 8 10 6 10 6 Or 10 6 0 10 6 0 10 6 B g

What are the degrees of freedom d f 4 A B C D E What is the critical value for this sample Round to four decimal places critical value 13 277 Complete the table by calculating the expected frequencies Observed Expected Frequency Frequency 14 Category A B C 14 13 13 5 8 13 13

the a 0 05 significance level test the claim that the responses occur with the same frequency Ho the test question responses occur with the same frequency Ha at least one question response occurs with a different frequency Response A B C D E Observed Expected Frequency Frequency 12 23 24 21 9 0 E E B What is the x test statistic for this data Round to four decimal places x2 What is the n yalue Round to four decimal places Part 2 of

15 An ecologist working with the New Jersey Department of Environmental Projection has been tasked with monitoring the water quality at beaches near Monmouth University She has recruited some of her friends to measure the concentration of Enterococcus faecalis a type of bacterium found in the gastrointestinal tract of humans and other mammals at six total beaches Over the course of several months they collected 13 samples from each beach The local nonprofit funding the research is interested in whether the log concentration of Enterococcus faecalis differs amongst the six beaches To begin the ecologist wants to determine if there is a difference in log concentration between beaches 2 and 4 Use the R printout to answer the following questions a Based on the boxplots does it appear that the log concentration of Enterococcus faecalis at beach 2 is Normally distributed Explain your reasoning according to the boxplot we can see that the log concentratio of the enterococcus facealis at beach 2 is not normally distributed due to the median box being closer to the bottom of b What test could the ecologist use to test for a difference between the two beaches A T test would be optimal in this scenario c What is the test statistic for the test you identified in the previous part How is it computed

Identify the following statements as true or false Part 1 of 4 If P 0 03 the result is statistically significant at the a 0 02 level The statement is Choose one true false Part 2 of 4 X If P 0 03 the null hypothesis is rejected at the a 0 02 level The statement is Choose one Y

6 In Q1 what is the P value for the ANOVA that tests for equality of the population means of the three treatments P value 0 4173 a Less than 0 01 b Between 0 01 and 0 05 c Between 0 05 and 0 10 d Greater than 0 10

9 True False Interchanging the degrees of freedom for the F distribution changes the distribution so order of parameters is very important a True b False

Question 3 Since Hill Valley High School eliminated the use of bells between classes teachers have noticed that more students seem to be arriving to class a few minutes late One teacher decided to collect data to determine whether the students and teachers watches are displaying the correct time At exactly 12 00 noon the teacher asked 9 randomly selected students and 9 randomly selected teachers to record the times on their watches to the nearest half minute The ordered data showing minutes after 12 00 as positive values and minutes before 12 00 as negative values are shown in the table below Students 4 5 3 0 0 5 0 0 0 5 0 5 1 5 5 0 Teachers 2 0 1 5 1 5 1 0 1 0 0 5 0 0 0 5 a Construct parallel boxplots using these data b Based on the boxplots in part a which of the two groups students or teachers tend to have watch times that are closer to the true time Explain your choice c The teacher wants to know whether individual students watches tend to be set correctly She proposes to test H u 0 versus H 0 where u represents the mean amount by which all student watches differ from the correct time Is this an appropriate pair of hypothesis to test to answer the teacher s question Explain why or why not Do not carry out the test

Quantitative variables are numerical values for which arithmetic operations such as means make sense It is usually a measure of some sort Categorical variables simply count which of several categories a person or thing falls Question 1 Are the following categorical or quantitative a zip codes e subjects listed according f students listed by to gender b list of subject heights social security number c the ages of several subjects recent test scores d the times it takes to make a button hole g students listed by

The area under the standard normal curve is 1 The standard deviation of the standard normal curve is 1 The mean of the standard normal curve is 0 5 What is the rule that describes 1 2 and 3 standard deviations from the mean Question 2 There are 4 basic typ problems 5 Students at the fine arts academy view on average five movies per semester with a standard deviation of two movies a What proportion of the students view more than six movies per semester b What proportion of the students view between 3 and 8 movies per semester c What proportion of the students view less than two movies per semester d What number separates the bottom 15 from the rest

Out of 600 people sampled 66 preferred Candidate A Based on this estimate what proportion of the voting population p prefers Candidate A Use a 99 confidence level and give your answers as decimals to three places

1 Single Sample T test A researcher would like to study the effect of alcohol on reaction time It is known that under regular circumstances the distribution of reaction times is normal with 200 A sample of 10 subjects is obtained Reaction time is measured for each individual after consumption of alcohol Their reaction times were 219 221 222 222 227 228 223 230 228 and 232 Use a 0 05

You are performing a Chi Square test with a level of significance of a 0 93 and degrees of freedom of 13 find the critical value to 4 decimal places Critical value is

A population of values has a normal distribution with 218 7 and o 95 1 You intend to draw a random sample of size n 48 Find the probability that a single randomly selected value is greater than 236 5 P X 236 5 Find the probability that a sample of size n 48 is randomly selected with a mean greater than 236 5 P M 236 5 Enter your answers as numbers accurate to 4 decimal places Answers obtained using exact z scores or Z scores rounded to 3 decimal places are accepted

Suppose a vector x exists in your workspace Which of the following commands will always output a logical vector of the same length as x with all of its elements being FALSE For example if the length of x is 3 then the output of the command should be 1 FALSE FALSE FALSE rep FALSE x logical length x Ox FALSE O X X

Suppose a logical vector x exists in your workspace Which of the following commands results in output identical to the output of all x O any x O any x O any x identical x TRUE

What is the output when you subset a numeric vector at an index greater than the length of the vector O NULL NaN

Is it possible to decrease the length of a vector using subsetting without redefining the entire object For example redefining the entire object in this case refers to assignment such as obj OTHER OBJECT O No

Suppose a numeric vector x exists in your workspace Which of the following commands will output a logical vector that indicates which elements of x are equal to either 2 or 3 x 2 x 3 x 2 3 O x 2 x 3 Ox 213

A Sebastian city official would like to estimate the average monthly rent of all rental units in Sebastian using a 96 confidence interval The standard deviation of the monthly rent of all rental units in Sebastian is known to be 63 67 How large a sample should the official select so that the estimate for the mean monthly rent is within 8 09 of the true population mean monthly rent 0336 O262 O168 0411

In a left tailed hypothesis test for a population mean where the population standard deviation is known the test statistic for a random sample of size 57 was calculated to be 1 9 Determine the p value for th test 0 9713 O 0 0287 0 0018 O 0 2643

A Type 2 error is made when O the alternative hypothesis is not rejected when it is false O the null hypothesis is not rejected when it is false O the null hypothesis is rejected when it is true O the alternative hypothesis is rejected when it is true

Grade Subject Math 9th Grade 10th Grade Total 7 10 Science 29 11 English 23 30 What s the joint relative frequency a 9th grader liked math What s the marginal relative frequency of 9th graders surveyed Given a student was in 10th grade what s the likelihood the student preferred English Given the subject was Science what s the likelihood the student was a freshman 96 96 Social Studies 11 9 96 Total 50

Question 10 Frequency Here again is the histogram showing the distribution of 50 ages at death due to trauma accidents and homicides that occurred in a certain hospital during a week 18 16 14 208642 12 10 20 30 40 T 50 Age 60 70 80 90 For the data described by the above histogram a the median will be bigger than the mean b the median will be smaller than the mean c the median and the mean will be about the same

Question 2 Here is a data set 62 52 66 60 51 89 60 62 68 51 83 75 86 66 59 55 61 50 63 65 61 64 58 68 71 66 72 77 76 59 You are examining the data with a stem and leaf plot Here is the start of the plot Finish the plot You may need to scroll to the right to see the full data set 5 01125899 6 1 00112234566688 7 12567 8 1 Question Help Post to forum

Score 0 16 1 16 answered Question 3 Here is a data set 41 27 41 28 49 38 31 31 30 38 44 39 34 43 45 37 34 31 26 33 You are examining the data with a split stem and leaf plot To make a split stem plot use digits 0 4 in the first row and 5 9 in the second row This is a way of changing the scale to 5 instead of 10 Here is the start of the plot 21678 31 0111344 317889 41 41 What should be entered in the second to last row of this table 41 Question Help Video Post to forum Submit Question

Homework 4 4 Score 0 8 0 8 answered Question 4 The owner of a small deli is trying to decide whether to discontinue selling magazines He suspects that only 14 1 of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable Before making a final decision he decides that for one day he will keep track of the number of customers that buy a magazine Assuming his suspicion that 14 1 of his customers buy a magazine is correct what is the probability that exactly 2 out of the first 13 customers buy a magazine 0000 0 291379 0 272906 0 293687 0 284900 0 287741 0 290509 Question Help Post to forum Submit Question

Question 3 T A recent study surveyed 1 358 households asking if the residents rented or owned and if the residents included dependents The results are summarized below 1 or More Dependent No Dependents Total Homeowner 479 216 695 Renter 294 663 Total 848 510 1 358 a What number of households reported having 1 or more dependent and renting Fill in the missing entry in the table b What percent of the renters reported having no dependents Round your percentage to 2 decimal places c Someone uses the table and calculates percent 216 510 42 35 Which is the correct interpretation of this 42 35 of homeowners reporting having no dependents 42 35 of people with no dependents reported being homeowners 42 35 of people surveyed were homeowners with no dependents None of these are correct

Question 12 6 6 28 4 38 5 72 15 Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day Activities of dolphin 2013 The numbers in the table represent the number of groups of dolphins that were partaking in an activity at certain times of days Period Activity Morning Noon Afternoon Evening Total Traveling Feeding Socializing Total Round all of your answers to 4 decimal places What is the probability that a dolphin group is partaking in feeding P feeding 14 0 9 23 13 39 56 88 10 62 79 189 What is the probability that a dolphin group is around at noon P noon MTH 43 22063 Statis What is the probability that a dolphin group is partaking in feeding given that it is noon P feeding noon What is the probability that a dolphin group is around at noon given that it is partaking in socializing P noon socializing What is the probability that a dolphin group is around in the afternoon given that it is partaking in traveling P afternoon traveling What is the probability that a dolphin group is around in the afternoon and is partaking in traveling P afternoon and traveling

Homework 4 4 Score 0 8 0 8 answered Question 2 Assume that a procedure yields a binomial distribution with a trial repeated n find the probability of k 3 successes given the probability p 0 58 of success on a single trial Report answer accurate to 4 decimal places P X k Question Help Post to forum Submit Question 15 times Use GeoGebra to