Probability Questions and Answers

A researcher is running rats through a maze but doesn t include the time for one rat that took a nap Which kind of selective reporting is going on O not reporting data for all subjects in the sample Obad sampling not reporting results for all the variables measured comparing things that are not comparable

Which of the following factors is most likely to lead to inaccurate results in a study field of study research techniques bias O validity O reliability

A marine diesel company produces one engine a month One year in January they add a turbocharger to the design and at the end of the year they want to compare the horsepower from this year s production to last year s production Which of the following is the appropriate approach OTwo sample t test Fisher Exact Test O Geometric mean Adiusted Wald interval

In 1936 a polling company called people on their telephones to measure who would win the presidency They confidently predicted Alf Landon would win At that time only the wealthy had telephones Which kind of selective reporting was going on O not reporting data for all subjects in the sample Obad sample not reporting results for all the variables measured comparing things that are not comparable

A team of researchers investigating cancer risks identified participants for a study which divided the participants into those who began an exercise program and quit smoking and another group where participants did not exercise or quit smoking What is a possible issue with one conclusion of this study stating that exercise decreases the risk of cancer There is no correlation between smoking and cancer There is no correlation between exercise and cancer The researchers assumed that smoking and exercise are associated with cancer risk The cessation of smoking could be the factor that had the greater impact in the reduced risk

One company sells a common chemical product used to kill ants in kitchens You work for a different company and are asked to develop an alternative All of your tests show that your alternative is no more effective than the current product What do you do to avoid selective reporting Select all that apply Report your results that show no evidence for your product being an improvement Run a second but different test The second test does make your product look better Report the results of both tests Tell your boss that the alternative is better without showing the results of your tests Keep the results to yourself and design a different test that might show your alternative is better Write a report explaining why you believe your alternative is better despite the lack of evidence

A college professor hypothesizes that students who study will pass a test while those who do not will fail With a sample of 12 students 1 did not study but passed 4 did not study and failed 7 studied and passed and 0 studied but failed What is the p value and the result OP 0 10 hypothesis not proven OP 0 10 hypothesis demonstrated OP 0 01 hypothesis not proven OP 0 01 hypothesis confirmed

If four out of five prototype jet engines run successfully what is the 95 confidence interval for the proportion of production engines that will run successfully if nothing is improved 0 36 0 98 0 23 0 88 0 64 0 96 O 0 51 0 83

Several new amateur recreational fishermen are given a new fish finding sonar to test how long it takes them to land a fish using it Their times are 26 43 38 241 and 35 minutes Which of the following is the appropriate way to report the results O Geometric mean of 51 minutes O Geometric mean of 77 minutes O Mean of 77 minutes O Mean of 51 minutes

Choose the words that best complete the sentence A produce sample can help ensure the results are not misleading The sample may be good but can still either intentionally or unintentionally

Use the union rule to answer the question If n A 4 n B 9 and n ANB 3 what is n AUB n AUB Type a whole number

N 0 2 3 2010 Gynyon Inc A comparison of means is done using the z test The resulting z score is 1 The area of the shaded area on the left the left tail is 0 1587 What is the probability of observing the sample means are equal when using the x test O 0 1587 O 0 3174 O 1 0000 O 1 0000

In general as the sample size decreases the confidence interval O increases decreases either increases or decreases remains the same

A random sample of 50 students sent a mean of 38 text messages in a day with a standard deviation of 12 Using the table below find the 90 confidence interval 35 21 to 40 79 35 67 to 41 33 33 63 to 42 37 Confidence Level z value 1 645 1 960 2 576 90 95 99

Each year a diesel engine manufacturing plant tests a sample of twenty five of their engines to make sure the horsepower is to specification This year the average was 2 538 horsepower with a 99 confidence interval of 2 494 2 582 If they do not change any processes for next year s manufacturing run what is the probability that the average horsepower next year will be outside this range O 1 0 0 1 O 5 10

What does a 99 confidence interval mean If you were to take an infinite number of samples of the same size as the original 99 of them would have a mean within the interval O The true mean will be within the interval 99 of the time O There is a 99 chance that the interval is right If you take another sample later 99 of the time the mean of that sample will fall within the interval

Your alpha level is 0 05 The probability of observing two sample means that you have gathered if the means of the population are the same is 0 04 Which statement below is true O You will accept that the null hypothesis that the means of the populations are the same You will reject the null hypothesis that the means of the population are the same There is no conclusion you can make in this situation Reject both the null and the alternate hypothesis

The average yield for corn crops is 180 bushels per acre with a standard deviation of 38 bushels an acre You carefully obtain the correct mean and standard deviation of the sampling distribution but have forgotten how many corn crops you observed for the sample If the sampling distribution had a mean of 180 and a standard deviation of 4 9 how many corn crops did you observe Round to the nearest whole number 8 O60 O180 05

Select the terms that best complete the statement At a security firm the mean salary of the employees is 53 000 with a standard deviation of 25 000 If you observed the salaries of 40 randomly selected employees the mean of the sampling distribution would be and the standard deviation of the sampling distribution would be

Select the terms that best complete the statement A new private school opened in your neighborhood Initially enrollment was low but over the years the number of students grew The average grade level is 3 5 with a standard deviation of 1 5 If the grades of 45 randomly sampled and the standard deviation of the sampling students are obtained the mean of the sampling distribution is distribution is

Select the terms that best complete the sentence The average age of all employees of a business is 53 with a standard deviation of 12 5 If the age of 36 randomly sampled employees is obtained the mean of the sampling distribution is and the standard deviation of the sampling distribution is

14 X In order to support the alternative hypthesis the obtained value must be O Larger than the critical value O Smaller than the critical value O Larger than 5 Smaller than 5 SUBMIT

Among the entire student body of 3 512 students 2 156 have a pet at home You want to know if a higher proportion of boys have pets at home when compared to the entire student body and decide upon a 0 01 level of significance Of a sample of 52 male students 35 have a pet at home Perform the z test and interpret your results Alpha a Za 0 1 0 05 0 01 O The z score is 0 874 You should reject the null hypothesis The z score is 0 874 You should not reject the null hypothesis The z score is 0 874 You should reject the null hypothesis The z score is 0 874 You should not reject the null hypothesis 24 1 28 1 645 1 645 1 96 2 33 2 575

Which of the following sets of hypotheses is incorrect O Ho M220 H M 20 H M 20 H M 20 Ho M20 H M 20 Ho M 20 H M 20

Suppose the hypothesis set is Ho M M Ha M M Provide the rejection region for it If the p value is 0 22 and the alpha is 0 02 what would you conclude Oright tail reject the null Oright tail fail to reject the null O left tail fail to reject the null Oleft tail reject the null

A researcher wants to know if studying improves scores and decides to set up a hypothesis test with alpha equal to 0 05 They randomly select students who study before tests and compare the sample grade average against the average test score of all students nationwide In the end the researcher determines that the sample average had a 0 08 probability of occurring if the null hypothesis is true What should the researcher conclude and what type of error might they be making Do not reject the null Type I error Do not reject the null Type Il error O Reject the null Type I error O Reject the null Type Il error

10 a In a game of poker 5 card han A flush is a 5 card hand that i A full house is three of a kind What is the probability of gettin Answer as a percent

If the hypotheses are Ho M 40 H M 40 what would you conclude at a p value 0 10 and alpha 0 0 There is no evidence to support that the mean is less than 40 There is no evidence to support that the mean is greater than 40 There is evidence to support that the mean is less than 40 There is evidence to support that the mean is greater than 40

Managers of a sports arena s parking garage keep track of the duration of time customers park their cars in the garage Shown in the stem and leaf display below is a sample of such parking durations in minutes For this sample 22 of the durations were from weekday use of the garage and 25 were from weekend use Answer the questions that follow Parking durations minutes Weekday Weekend 87741 15 45 89 98653 16 4 4 6 6 6 79 17 00003345 98886100 730 18 3799 6 19 48 Key 151 1 15 4 154 a What were the ranges of parking durations for the two groups Weekday Weekend b Which group had the higher median parking duration The medians were the same OWeekday Weekend c Which group had more parking durations in the 170s OWeekday Weekend OEach had the same

1 In a survey of U S men the heights in the 20 29 age group were normally distributed with a mean of 69 4 inches and a standard deviation of 2 9 inches Find the probability that a randomly selected study participant has a height that is between 66 and 72 inches

3 A group of Brigham Young University Idaho students Matthew Herring Nathan Spencer Mark Walker and Mark Steiner collected data on the speed of vehicles traveling through a construction zone on a state highway where the posted speed was 25 mph The recorded speed in mph of 14 randomly selected vehicles is given below 20 24 27 28 29 30 32 33 34 36 38 39 40 40 a Iso known Which method should we use to find a confidence interval Verify the assumptions are satisfied for that method b Assuming speeds are approximately normally distributed with no outliers construct a 95 confidence interval for the true mean speed of drivers in this construction zone Interpret the interval C Construct a 99 confidence interval for the true mean speed of drivers in this construction zone Interpret the interval

For a fishing trip Kira is going to choose lures to put in her tackle box She has 6 lures that are buzzbaits and 7 that are spinnerbaits In how many ways can she choose 5 lures if 1 or fewer must be spinnerbaits If necessary consult a list of formulas

Scott has a deck of 10 cards numbered 1 through 10 He is playing a game of chance This game is this Scott chooses one card from the deck at random He wins an amount of money equal to the value of the card if an even numbered card is drawn He loses 7 if an odd numbered card is drawn If necessary consult a list of formulas a Find the expected value of playing the game dollars b What can Scott expect in the long run after playing the game many times He replaces the card in the deck each time O Scott can expect to gain money He can expect to win dollars per draw O Scott can expect to lose money He can expect to lose dollars per draw Scott can expect to break even neither gain nor lose money

Smoke detectors An insurance company offers a discount to homeowners who install smoke detectors in their homes A company representative claims that 80 or more of the policy holders have smoke detectors You draw a random sample of 8 policy holders d If exactly 80 of the policy holders have smoke detectors what is the probability that at most 6 of the 8 sampled policy holders have smoke detectors use the binomial probability calculator to solve the problem

Claim Fewer than 96 of adults have a cell phone In a reputable poll of 1107 adults 86 said that they have a cell phone Find the value of the test statistic The value of the test statistic is Round to two decimal places as needed

t try 1 of 2 pts See Details for more ry this question below

A factory produces protein bars clai actual weights are normally distribu ounces Each morning a carton of 2

7 A bag contains 3 orange marbles 3 green marbles 5 red marbles and one yellow marble Miranda randomly selects 7 of them Find the probabilit of the given events a She gets one orange marble 2 green marbles 3 red marbles and the yellow marble Answer 11 36 X Check Clear b She gets all the orange marbles

12 Two dice one red one green are cast and the uppermost numbers are observed Test the given events for independence in each case O Independent Dependent a b c d e E The red die comes up 6 F The green die comes up odd E The red die comes up 5 F The sum is odd E The red die comes up 2 F The sum is 8 Independent O Dependent E The sum is 2 F The green die comes up odd Independent O Dependent E Neither die is 5 F The die show different numbers O Independent O Dependent Independent O Dependent

Condition improved I No change N Condition worse W Total c P I Assume that a participant is selected at random Let M be the event that the participant used the medication L the event that the participant used th placebo I the event that the participant s condition improved and so on as shown by the letters in the headings a P I M Check Clear Give the exact answer not a decimal approximation Check Clear Used medication M Used placebo L 20 280 340 2500 40 2820 400 5600 b P M I Give the exact answer not a decimal approximation Check Clear d P M Give the exact answer not a decimal approximation Check Clear Give the exact answer not a decimal approximation e Test the events I and M for independence O Independent O Dependent Total 300 2840 2860 6000 O Independent

0 6 pts 100 weights of newborn babies are normally distributed with a mean of 8 5 pounds and a standard tion of 2 pounds A random sample of 25 newborns are selected n the Central Limit Theorem be applied stion 4 No because the standard deviation is too low Yes because the sample size is more than 20 Yes because even though the sample size is less than 30 the original distribution is normally distributed No because the sample size is less than 30 ind the standard deviation of the mean of the 25 newborn babies Round to 1 decimal place What is the probability that the mean weight of this sample is less than 7 5 pounds Round to 4 decimal ces What is the probability that the mean weight of the sample is between 7 5 and 8 pounds Round to 4 cimal places Find the 20th percentile of mean sample weights Round to 3 decimal places Detail If one newborn baby is randomly selected find the probability that his her weight is less han 7 5 pounds Bound to d decimal plac

Question 14 A half hour daytime tv show has an average o of commercials follows a normal distribution a Find the percent of half hour daytime tv sh nd answer a probability n

Find the exact probability from the z table a P Z 1 b P 0 5 Z 1 c P Z 0 d P Z 0 5 e PIZ 0 65

uestion 2 nsider a normal distribut

How smart is your phone A random sample 169 385 329 249 349 199 135 Alle 269 149

If a card is drawn from a deck of 52 playing cards then what is the probabiltiy of getting an Red or a Queen

All of the possibilities for his schedule are shown in the tree diagram below Anatomy Statistics Psychology Economics Sociology Biology Psychology Economics Sociolc What is the probability that his social sciences class is not Economics

Probability Scores 0 1 3 7 8 13 14 0 02 0 15 0 05 0 02 0 09 0 4 0 27 Find the expected value of the above random variable

Ignoring twins and other multiple births assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0 5 If the first 5 children born are girls what is the probability the next born child is a boy 0 50 0 75 0 80 0 99 cannot tell based on this information

Suppose that we ve decided to test Clara who works at the Psychic Center to see if she really has psychic abilities While talking to her on the phone we ll thoroughly shuffle a standard deck of 52 cards which is made up of 13 hearts 13 spades 13 diamonds and 13 clubs and draw one card at random We ll ask Clara to name the suit heart spade diamond or club of the card we drew After getting her guess we ll return the card to the deck thoroughly shuffle the deck draw another card and get her guess for the suit of this second card We ll repeat this process until we ve drawn a total of 15 cards and gotten her suit guesses for each Assume that Clara is not clairvoyant that is assume that she randomly guesses on each card Answer the following If necessary consult a list of formulas a Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution that is the expectation of the relevant random variable Do not round your response 0 b Quantify the uncertainty of your estimate by giving the standard deviation of the distribution Round your response to at least three decimal places