Statistics Questions

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

Thanks to an initiative to recruit top students an administrator at a college claims that this year s entering class must have a greater mean IQ score than that of entering classes from previous years The administrator tests a random sample of 19 of this year s entering students and finds that their mean IQ score is 118 with a standard deviation of 12 The college records indicate that the mean IQ score for entering students from previous years is 112 mean IQ Is there enough evidence to conclude at the 0 05 level of significance that the population score U of this year s class is greater than that of previous years To answer assume that the IQ scores of this year s entering class are approximately normally distributed Perform a one tailed test Then answer the questions below Carry your intermediate computations to three or more decimal places a State the null hypothesis Ho and the alternative hypothesis H1 Ho H b Determine the type of test statistic to use Z t Chi square F Degrees of freedom if applicable side igas c Find the value of the test statistic Round to three or more decimal places d Find the critical value Round to three or more decimal places zizotiony Hun er en au of of21632 1240 to sqva sit stimplod d Yes No e Can we conclude that the mean IQ score of this year s class is greater than that of previous yea 20 916002 110 sv en br

A college recently advertised that 93 of its students graduate debt free A student advocacy organization thinks that the college s claim is unlikely The organization collected a random sample of 1537 recent graduates from the college and found that 90 9 of the sample graduated without any student debt Let a 0 02 and employ the critical value method to test the hypothesis that the proportion of all students from this college that graduate debt free is different than 93 State the null and alternative hypothesis for this test O Ho p 0 93 H p 0 93 O Ho p20 93 H p 0 93 O Ho p 0 93 H p0 93 Ho p0 93 H p 0 93 Determine the critical value s for the hypothesis test O2 33 O 2 17 2 17 O 2 33 2 33 O 1 28 1 28 Determine test statistic for the hypothesis test O 3 84 O 4 36 O 3 23 O 2 85 etermine the appropriate conclusion for this hypothesis test O The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all students at the college that graduate debt free is 0 93 and thus we conclude that the proportion of all students at the college that graduate debt free is likely different than 0 93 The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of all students at the college that graduate debt free is different than 0 93 and thus we conclude that the proportion of all students at the college that graduate debt free is likely equal to 0 93 D The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of all students at the college that graduate debt free is different than 0 93 and thus we conclude that the proportion of all students at the college that graduate debt free is likely different than 0 93 the ull hypothesis that the proportion

The following confidence interval gives a range of likely values for the average nightly tip income for servers at an upscale restaurant 138 178 Determine the value of that was used to construct this confidence interval O 20 158 O 40 O 138

A travel agency plans to develop a new ad campaign to entice visitors to come to the Treasure Coast As a part of the new campaign the agency would like to advertise the warm ocean water along the Treasure Coast but would like to do so accurately They hire a statistics student to record the water temperature on a randomly selected sample of 10 days The water temperature of each day is recorded below 74 8 85 1 76 5 71 8 72 3 77 1 80 80 8 84 9 78 8 Using a 99 confidence level determine a confidence interval for the average water temperature along the Treasure Coast O 74 9 81 5 O 76 2 80 2 O 75 5 80 9 73 4 83

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

Suppose that follows a chi square distribution with 28 degrees of freedom Use the ALEKS calculator to answer the following a Compute P 20 x 43 Round your answer to at least three decimal places P 20 x 43 b Find such that P x k 0 025 Round your answer to at least two decimal places k X

According to a Pew Research Center poll conducted last year 63 of American adults say that young adu should be financially independent by age 22 A social scientist would like to test this claim He found that 298 out of a random sample of 484 America adults said that young adults should be financially independent by age 22 Calculate the test statistic for the following set of hypotheses Ho p 0 63 H p0 63 O 0 65 O 0 94 O 0 65 O2 50

The average annual car insurance premium yearly cost in Florida is among the highest in the nation To estimate the average annual car insurance premium in Florida a data analyst contacted a random sample of 285 car owners in Florida and found that the average annual car insurance premium of the sample was 1 833 From previous research standard deviation of the distribution of all annual car insurance premiums in Florida is known to be 249 Using a 98 confidence level determine a confidence interval for the average annual car insurance premium in Florida 1800 99 1865 01 O 1804 09 1861 91 O 1795 01 1870 99 1708 60 1967 21

Determine the value of t necessary to construct a confidence interval when the sample size is 39 and the level of confidence is 90 O 1 6849 O 1 6859 039744

A certain brand of mosquito repellent claims that it will effectively repel A local biologist thinks that the company s claim is exaggerated and the length of time for which this brand of mosquito repellent is effective is actually less than 4 hours To test his hypothesis the biologist devised a randomized sample of 125 trials and found that the mosquito repellent was effective for 3 77 hours on average Use the p value method to test the hypothesis that the mean effective length of time of this brand mosquito repellent is less than 4 hours using a significance level of 5 Assume the standard deviation of the distribution of all times for which this brand of mosquito repellent is effective is known to be 1 48 hours State the null and alternative hypothesis for this test O Ho 4 H 4 O Ho 24 H 4 O Ho 4 H 4 O Ho 4 H 24 Determine the test statistic for the hypothesis test O 1 74 O 1 69 O 4 34 O 3 28 Determine the p value for the hypothesis test O 0 1326 O 0 9591 O0 0117 0 0409 termine the appropriate conclusion for this hypothesis test The sample data provide sufficient evidence to reject the null hypothesis that this brand of mosquito repellent is effective for at least 4 hours and thus we conclude that the company s claim that that the mosquito repellent lasts for at least 4 hours is likely false The sample data do not provide sufficient evidence to reject the alternative hypothesis that this brand of mosquito repellent is effective for less than 4 hours on average and thus we conclude that he company s claim that the mosquito repellent is effective for at least 4 hours is likely false the sample data provide sufficient evidence to reject the alternative hypothesis that this brand of osquito repellent is effective for less than 4 hours on average and thus we conclude that the mpany s claim that the mosquito repellent is effective for at least 4 hours is likely true sample data do not provide sufficient evidence to reject the null hypothesis that this brand of quito repellent is effective for at least 4 hours and thus we conclude that the company s claim

The Student s t distribution is used to construct a confidence interval when O working with a proportion O working with a mean and the standard deviation is unknown O working with a mean and the standard deviation is known O the sample size is smaller than 30

Due to the COVID 19 pandemic many college classes have been moved online The college would like to estimate the proportion of students that have access to reliable high speed internet A random sample of 529 college students was selected and it was found that 347 students out of the sample had access to reliable high speed internet Using a 99 confidence level determine a confidence interval for the proportion of all students at the college who have access to reliable high speed internet O 60 79 70 4 O 60 28 70 92 O 61 55 69 64 O 62 2 68 99

If it is determined that a confidence interval has a margin of error that is too large a researcher can decrease the margin of error by O decreasing sample size or decreasing the level of confidence O decreasing sample size or increasing the level of confidence O increasing the sample size or increasing the level of confidence O increasing sample size or decreasing the level of confidence

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

A Type 1 error is made when O the alternative hypothesis is not rejected when it was false O the alternative hypothesis is rejected when it was true O the null hypothesis is not rejected when it was false O the null hypothesis is rejected when it was true

Last year the mean price of a single family home in Sebastian was found to be 126 197 This year a real estate researcher would like to determine if the mean single family home price in Sebastian is less than 126 197 O Ho O Ho O Ho P of 126197 H 126197 126197 H 126197 126197 H 126197 196197 H 196197

The significance level of a hypothesis test which is denoted by a is the probability of O making a sampling error O making a Type 1 error O making a Type 2 error O making a non sampling error

In a poll of 125 randomly selected U S adults 66 said they favored a new proposition Based on this poll compute a 95 confidence interval for the proportion of all U S adults in favor of the proposition at the time of the poll Then find the lower limit and upper limit of the 95 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to two decimal places If necessary consult a list of formulas Lower limit Upper limit X

Which of the following statements is a possible null hypothesis O The population mean is equal to 62 O The population mean is not equal to 62 O The population mean is greater than 62 O The sample mean is greater than or equal to 62

The width of a confidence interval is affected by the O sample size O the sample mean O the population mean O Type I error

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

3 Show that any subset of 55 distinct positive integers less than 101 must contain two integer which differ by exactly 9

Volunteer Gender Age 1 Male 21 Female 20 Male 47 Female 60 Female 62 Male 61 Male 58 Female 44 Male 44 Female 24 Male 23 Female 46 2 3 4 5 6 7 8 9 Question 4 Researchers who are studying a new shampoo formula plan to compare the condition of hair for people who use the new formula with the condition of hair for people who use the current formula Twelve volunteers are available to participate in this study Information on these volunteers numbered 1 through 12 is shown in the table below 10 11 12 a These researchers want to conduct an experiment involving the two formulas new and current of shampoo They believe that the condition of hair changes with age but not gender Because researchers want the size of the blocks in an experiment to be equal to the number of treatments they will use blocks of size 2 in their experiment Identify the volunteers by number that would be included in each of the six blocks and give the criteria you used to form the blocks b Other researchers believe that hair condition differs with both age and gender These researchers will also use blocks of size 2 in their experiment Identify the volunteers by number that would be included in each of the six blocks and give the criteria you used to form the blocks c The researchers in part b decide to select three of the six blocks to receive the new formula and to give the other three blocks the current formula Is this an appropriate way to assign IS

nfidence interval and interpret the results If using provide the description of the clicks you used Question 2 6 points In a random sample of eight people the mean commute time to work was 35 5 minutes and the standard deviation was 7 2 minutes Assuming the population is normally distributed find the margin of error and construct a 95 confidence interval Interpret the results If using Statcrunch provide the description of the clicks you used

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 11 The frequency table below shows the scores of a group of students on a 10 point quiz The frequency is the number of students who got that score Frequency Test Score 3 4 5 6 7 8 9 10 3 2 1 0 4 3 4 3 The mean score on this test is The median score on this test is

Question 4 Actors Home MyPCC The following stem and leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress Stems years 98753221 3 00113344455778 88776543322100 4 6651 5 210 6 6 7 8 Actresses 2 146667 years 11129 a What is the age of the youngest actor to win an Oscar 011 4 0 DUL Homepage MTH 243 22063 Statistics I b What is the age difference between the oldest and the youngest actress to win an Oscar c What is the oldest age shared by two actors to win an Oscar Google Yaho

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 Work 2 1 2 2 2 7 except 2 2 3 and 2 2 4 Question 8 Frequency The shape of the distribution of the data pictured below could best be described as OO S data Uniform Approximately Symmetric Skewed right Skewed left 5

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

The histogram below shows the odometer readings in miles of Honda Civic automobiles listed for sale on the Seattle Times Web site on November 26 2003 of cars 00 8 15 0 n 90000 mean 180000 Which of the following terms apply to this histogram Select all that apply symmetric left skewed Oright skewed median mileage miles Which measure of center is most appropriate for this data BIL Homepage MTH 243 22063 Statistics I Which measure of spread is most appropriate for this data standard deviation IQR

Question 12 The highway mileage mpg for a sample of 5 different models of a car company can be found below Find the mean median mode and range 21 23 26 28 28 30 Mean Median Mode Range Question Help Post to forum Submit Question

Question 15 A survey taken in a large statistics class contained the question What s the fastest you have driven a car in miles per hour The five number summary for the 87 males surveyed is min 55 Q1 95 Median 110 Q3 120 Max 155 Should the largest observation in this data set be classified as an outlier Yes No OO Question Help Or

Question 14 Given the 5 number summary for a set of data find the IQR Interquartile Range Q1 30 Minimum 0 IQR Median 49 Question Help Video Post to forum Q3 69 Maximum 100

Frequency 10 8 2 1 6 11 16 21 26 data Q Based on the histogram above what is the frequency of the class containing the value 22 Question Help Post to forum Submit Question 31

Frequency 10 8 6 A 2 11 16 21 26 31 date Based on the histogram above what is the class width Class width 1 6 What is the sample size Sample size Question Help Post to forum

The kicker for San Francisco Phil Dawson is lined up on the 35 yard line waiting to punt the ball on fourth and long to the opposite side of the field How hard does he have to kick the ball to have it bounce within the 20 yard line if he kicks the ball at a 75 angle Football Field is a total of 100 yards long and assume to be within the 20 yard line it bounces at the 19 yard line

Use the following table of data to select the answer A market research study on motorcycles contains the following data for sales of motorcycles at various prices over the past month Price thousands of dollars P Sales of motorcycles S 5 6 22 43 A S 1 18S 28 43 r 0 26 CS 4 46P 2 14 r 0 99 E S 1 18P 28 43 r 0 26 7 8 9 10 11 36 50 46 29 39 19 Select the correct regression line and correlation coefficient for the data above Estimate all quantities to 95 two decimal places B S 1 18P 28 43 r 0 26 D S 4 46P 2 14 r 0 99

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 5 A CBS News poll conducted January 5 2017 among a nationwide random sample of 906 adults asked those adults about their party affiliation Democrat Republican or none and their opinion of how the US economy was changing getting better getting worse or about the same The results are shown in the table below better same worse 132 64 15 88 167 186 none 135 44 75 Republican Democrat Use the two way table above please answer the following questions Please enter your answers as fractions They do not need to be reduced a What fraction of all survey respondents identified themselves as affiliated with neither party b What fraction of all survey respondents thought the economy was about the same c What fraction of the those affiliated with neither party thought the economy was about the same d Among all survey respondents who thought the economy was about the same what fraction were affiliated with neither party e What fraction of all survey respondents were affiliated with neither party and thought the economy was about the same Question Help Post to forum

Question 8 About 2 of the population has a particular genetic mutation 100 people are randomly selected Find the standard deviation for the number of people with the genetic mutation in such groups of 100 Question Help Post to forum Submit Question

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

Homework 4 4 Score 0 8 0 8 answered Question 5 Y Matching questions ask you to match each question on the left with one of the choices on the right Not all choices on the right may be used For the binomial distribution match each statistic with its formula n is the number of trials p is the probability of success variance expected number of failures mean or expected number of successes standard deviation Question Help Post to forum Submit Question a nq b np rounded to an integer C npq d np e npq f n p

Homework 4 4 Score 0 8 0 8 answered Question 6 At a university 18 of students smoke a Calculate the expected number of smokers in a random sample of 130 students from this university please do not round your answer b The university gym opens at 9 am on Saturday mornings One Saturday morning at 8 55 am there are 30 students outside the gym waiting for it to open Should you use the same approach from part a to calculate the expected number of smokers among these 30 students No it is unlikely that smoking habits and waking up early to go to the gym on Saturday are independent Yes it is reasonable to believe that people who go to the gym when it first opens on Saturday mornings is a representative sample Question Help Post to forum Submit All Parts

Fill in the blank with an appropriate word or phrase If a sample is drawn in such a way that each time an item is selected each item in the population has an equal chance of being drawn the sample is called sample If a sample is drawn in such a way that each time an item is selected each item in the population has an equal chance of being drawn the sample is called sample a cluster stratified convenience random ntin Next

19 A psychologist from Austin Texas interested in sleep s effect on the ability to learn randomly selects high school students from the area s local high schools Half the students are randomly selected to sleep between 7 and 8 hours a night while the remaining half sleep as they normally would At the end of the study those students who got between 7 and 8 hours of sleep a night scored significantly higher on tests over the curriculum studied at their school From this the psychologist can conclude A Austin high school students getting between 7 and 8 hours of sleep per night score higher on tests over their curriculum B Students in the United States who get between 7 and 8 hours of sleep per night get better grades C Austin students who sleep between 7 and 8 hours per night get better grades D High school students getting between 7 and 8 hours of sleep per night score higher on tests over their curriculum E Since a placebo was not included in the study no significant conclusions can be made