Math 140 Exam 2
This poll was shown in July 2018. It shows a MOE (margin of error) of 3%, or 0.03. It shows poll results of issues that millennials care about most: Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%. What is the upper limit of the confidence interval for the proportion of millennials that care about Immigration? Write your answer as a proportion (decimal) and NOT as a percent. Do not Round.
0.2
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?
3.2%
This poll was shown in July 2018. It shows a MOE (margin of error) of 3%, or 0.03. It shows poll results of issues that millennials care about most: Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%. What is the confidence interval for the proportion of millennials that care about Healthcare?
(0.13, 0.19)
This poll was shown in July 2018. It shows a MOE (margin of error) of 3%, or 0.03. It shows poll results of issues that millennials care about most: Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%. What is the confidence interval for the proportion of millennials that care about Jobs/Economy?
(0.22, 0.28)
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 randomly selected members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Find the 90% confidence interval.
(2.166, 2.634)
How much sugar do reduced sugar cookies typically have? You take a random sample of 51 reduced-sugar cookies and test them in a lab, finding a mean sugar content of 3.2 grams and a standard deviation of 1.1 grams of sugar. Create a 99% confidence interval for the mean grams of sugar.
(2.7875, 3.6125)
Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community.
(3.77%, 8.70%)
The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 120 residents whose mean number of pounds of trash generated per person per week was 31.5 pounds and the standard deviation was 7.8 pounds. What is the confidence interval for the mean number of lbs of trash per person per week that is generated in the city?
(30.090, 32.910)
The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?
.1608 to .2392
This poll was shown in July 2018. It shows a MOE (margin of error) of 3%, or 0.03. It shows poll results of issues that millennials care about most: Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%. What is the lower limit of the confidence interval for the proportion of millennials that care about the Education? Write your answer as a proportion (decimal) and NOT as a percent. Do not Round.
0.13
Dem Now 50% Jan 49% Rep Now 40% Jan 43% The above picture shows the results of a survey in March 2018. The survey results showed that 50% of the survey felt that Democrats should control congress, while 40% felt that Republicans should control congress. Both have a Margin of Error of 2.95%. What is the upper limit of the confidence interval for the proportion of the population that believe that Republicans should control Congress? Write your answer as a proportion (decimal) and NOT as a percent. Do not Round.
0.4295
Dem Now 50% Jan 49% Rep Now 40% Jan 43% The above picture shows the results of a survey in March 2018. The survey results showed that 50% of the survey felt that Democrats should control congress, while 40% felt that Republicans should control congress. Both have a Margin of Error of 2.95%. What is the lower limit of the confidence interval for the proportion of the population that believe that Democrats should control Congress? Write your answer as a proportion (decimal) and NOT as a percent. Do not Round.
0.4705
In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of 0.3. What is the 90% confidence interval for the true mean length of the bolt?
2.814 to 3.1859
In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt?
2.864 to 3.136
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. What is the Lower Limit (LL) of the confidence interval for Biden?
41.5%
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. What is the Lower Limit (LL) of the confidence interval for Trump?
45.5%
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. What is the Upper Limit (UL) of the confidence interval for Biden?
50.5%
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. What is the Upper Limit (UL) of the confidence interval for Trump?
54.5%
150 accidents that required treatment in an emergency room were randomly sampled from hospitals across the country. 36% involved children less than 6 years of age. Find the 90% confidence interval to estimate the true proportion of all accidents requiring ER treatment that involve a child less than 6 years old. P-> p = The true proportion of all accidents requiring ER treatment that involve a child less than 6 years old . A-> Random? Yes, stated the sample was random. np ̂ = (150)(0.36) = 54 ≥ 10 nq ̂ = (150)(0.64) = 96 ≥ 10 N-> 1 proportion-z confidence interval I-> (0.2955 , 0.4245) C-> We are 90% confident that the true proportion of all accidents requiring ER treatment that involve a child less than 6 years old is between 0.2955 and 0.4245. Which of the PANIC steps are wrong / incomplete? Select all that apply
All are correct
The researcher picks 20 different small groups: a church group, a Democrat club, a student club, etc., each containing 100 people. Then the researcher makes sure that everyone from each group answers the survey question. The administrator goes into 9 classes from many subject areas and asks all the students in each of these 9 classes Jamie randomly selects 45 streets in Newhall and asks every person living on those streets The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
Cluster sampling
The researcher posts the survey on the Internet the survey question and waits until 2000 people have responded. The administrator stands by the front door of the admissions department and asks the first 250 students who walk in. Jamie asks her neighbors as they walk by her when she's walking her dog The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
Convenience sampling
Michelle, a teacher at Valencia High, wants to see how many students at Valencia High school will be attending COC. She gives the students in her U.S. History class a questionnaire to fill out that asks where they will be attending college. Identify the method of collecting data (census, simple random sample, systematic, convenience, voluntary response, cluster, stratified).
Convience
When the sample size increases, everything else remaining the same, the width of a confidence interval for a population parameter will:
Decrease
As the margin of error decreases, the width of the confidence interval
Decreases
Determine which brands of orange juice people prefer. Passerbys in a supermarket are asked to taste different brands without knowing which brand they are drinking, and which one they prefer.
Experiemtn
Compare the grades on a final math test between students who use a calculator and students who do not. Fifty students are recruited where 25 students are assigned to use a calculator and 25 students assigned to not use a calculator. The teacher assigns students to whether they use a calculator or not, using a computer randomization applet.
Experimetn
A sampling distribution just looks at 1 sample.
False
As the sample size increases, the standard error gets larger
False
If a sample is random, the sample value will be exactly the same as the population value.
False
In an experiment, the researcher only watches and arrives at a conclusion but does not interfere with the subjects.
False
It doesn't matter if the population is skewed, the distribution of sample means will always be bell shaped.
False
Random is not important in the central limit theorem.
False
Random samples should have at least 10 successes and at least 10 failures if we want our random sample percent to estimate the population percent. This means we will always need a data set size of exactly 20.
False
Random samples will be exactly the same as the population value.
False
The CLT only applies to sample means and does not apply to the distribution of sample percentages.
False
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. Because of the way the poll was conducted, I can use these results to generalize to all Latino voters in America.
False
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. Because of the way the poll was conducted, I can use these results to generalize to all voters in Florida.
False
The sample percentage from just a single data set is usually much closer to the population percentage than the center of a sampling distribution of sample percentages.
False
The standard deviation of a single data set and the standard error of a sampling distribution is the same number always.
False
There is human intervention in observations
False
We can establish cause and effect with observational studies
False
We do not need to study sampling variability, just take some voluntary response data, calculate the sample mean, and then just tell people it is the population mean.
False
A small sample size is part of a well-designed experiment.
False; A large sample size is better for comparison in a well-designed experiment.
You have sampled 25 randomly selected students to find the mean test score. A 95% confidence interval for the mean came out to be between 85 and 92. Which of the following statements gives a valid interpretation of this interval?
If this procedure were to be repeated many times, 95% of the confidence intervals found would contain the true mean score
In the construction of a confidence interval, as the confidence level required in estimating the mean increases, the width of the confidence interval
Increase
Which of the following is an advantage of confidence interval estimate over a point estimate for a population parameter?
Interval estimates take into account the fact that the statistic being used to estimate the population parameter is a random variable
If the standard deviation of a sample increases and you want the confidence interval width to remain the same, then the sample size must _____________.
NOT DECREASE OR STAY THE SAME MOST LIKELY INCREASE!!
The mean of the sampling distribution of the sample mean is:
NOT equal to the population mean divided by n. OR an approximation of the mean of the population.
The width of a confidence interval will be:
Narrower for 90% confidence than 95% confidence.
A study follows two groups of students, who are randomly selected from a school, for one year. Students decide which group to join depending on which category they feel they belong to: I watch more than 10 hours of TV per week OR I watch fewer than 5 hours of TV per week. Students who watch no television, or who watch between 5 and 10 hours a week, were excluded from participating in the study. The study records the average grades and the percent of students who participate in team sports. Is this an observational study or experiment?
Observational
In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confidence interval for the proportion of adults in the United States who say that their favorite sport to watch is football. Construct a 95% confidence interval and interpret its meaning using PANIC. P--> mu = 𝜇=μ=The true proportion of all US adults who watch football as their favorite sport. A--> Random stated in problem. 354 (number of successes) > 10 N--> One proportion Z confidence interval I--> (0.265 , 0.316) C--> We are 95% confident that between 26.5% and 31.6% of all US adults prefer to watch football as their favorite sport. Which of the PANIC steps are wrong / incomplete? Select all that apply
P & A
A Gallup poll conducted a random sample survey in 2005 asked 1006 Americans how many books did they read in the past year. Results of the survey indicated the mean to be 13.4 books, with a sample standard deviation of 16.6 books. Construct a 99% confidence interval and interpret its meaning. P--> mu = the true mean number of books read by 1006 Americans from 2004 - 2005 A--> random stated, n = 1006 > 30, all assumptions met N--> T Interval, or 1 samp t int I--> (11.05, 14.98) C--> we are 99% confident that the true mean number of books read by 1006 Americans from 2004 - 2005 is between 11.05 to 14.98 books.
P C & I
Which of the following are reasons that a sample may be a biased or unreliable sample. Choose all that apply.
PARTIAL!!! Trying to conclude that there is a cause-and-effect relationship when something else causes both. The funders of the project are partial to the results. The graphs are drawn in a way to mislead the reader. Two factors cannot be separated to determine which is the one that is responsible for the outcome.
A 1993 survey conducted by the local paper in Kansas City, Missouri, one week before election day asked voters who they would vote for in the City Attorney's race. Thirty-seven percent said they would for the Democratic candidate. On election day, 41% actually did vote for the Democratic candidate. The number 41% is a
Parameter
A phone-in poll conducted by a newspaper reported that 64% of those who called in watched the TV show South Park on Comedy Central. The unknown true percentage of American citizens who watch South Park is a
Parameter
The distribution of the values taken on by a statistic in all possible samples from the same population is called
Sampling distribution
The researcher gets the complete list from the Census Bureau and uses a computer to randomly select 2000 people. The administrator gets the complete list of students at the college and then uses a computer to randomly select 250 students. She then surveys these 250 students. She obtained an alphabetical list of all the residents in Newhall and numbered them. She then used the computer to generate random numbers to decide which people to question about their voting preferences. The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
Simple random sampling
A phone-in poll conducted by a newspaper reported that 64% of those who called in watched the TV show South Park on Comedy Central. The number 64% is a(n)
Statistic
A survey conducted by Raid asked whether the action of a certain type of roach disk would be effective in killing roaches. Seventy-nine percent of the respondents agreed that the roach disk would be effective. The number 79% is a
Statistic
Rick works for a sports equipment manufacturing company. He separates all the employees into men and women, and then chooses 28 women and 30 men to ask if they want changes to their medical insurance coverage. Identify the method of collecting data
Stratified
The researcher makes sure that the proportion of respondents from each state matches the proportion of each state's population to the US population. The administrator researches the ethnic make-up of the college and makes sure that the proportion of each ethnic group represented in the sample is the same as the corresponding proportion of that ethnic group at the college. She separates all residents of Newhall in men and women, then chooses 33 men and 29 women to ask ab out their vote The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
Stratified sampling
The researcher gets the complete list from the Census Bureau and surveys every 150,000th person on the list. The administrator gets the complete list of students at the college and surveys every 50th students on the list. she obtains a list of all residents of Newhall and decides to ask every 50th person on the list. The biologist orders the 15 million acres by latitude and then surveys every 100,000th acre on the list.
Systematic sampling
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Round your answers to two decimal places. The sampling distribution follows what kind of distribution?
T-distribution; Since the standard deviation is unknown, the sampling distribution is T.
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. The UL for Biden goes higher than the LL for Trump, so there may not be a lead for Trump according to this poll.
True
Which of the following are reasons that a sample may be a biased or unreliable sample. Choose all that apply.
The sample is not representative of the population. Self-Selected Sample. (Voluntary Sample) The sample size is too small. The wording of survey question influences the response.
Drew doesn't like eating raw carrots. He decides to provide his parents with qualitative data to support his opinion. Carrots taste dry is qualitative data.
True
If Alli wants to find out how long it takes her baby sister to fall asleep, she might use the time of day and noise levels as variables in her experiment.
True
If a scientist is studying a common type of snail and he or she says that the average length of these snails is 4.5 centimeters, his or her measurements are probably based on a study of more than 15 snails.
True
In observational study, the researcher relies more on data collected.
True
Random samples should be at least 30 or nearly normal if we want our random sample means to estimate the population means.
True
Random samples will often give very different sample means and sample percentages so they will all have variability.
True
Sampling distributions are very useful when studying inferential statistics.
True
Scientists collect evidence by making observations.
True
The average (center) of all the random sample means will be a good estimate of the population mean.
True
The average (center) of all the random sample percentages (proportions) will be a good estimate of the population percent.
True
The center of a sampling distribution is usually a more accurate estimate of the population mean than a sample mean from 1 sample.
True
The concepts of 99% confidence, confidence intervals, standard error and margin of error can all be better understood from studying sampling distributions.
True
The distribution of random sample means is normally distributed for sufficiently large samples.
True
The main difference between observational study and experiments is in the method and the way data is collected.
True
The picture shows a poll that was conducted targeting Florida Latino Voters from August 31 to September 6, 2020. For the purposes of this assignment, we will assume that the poll was conducted randomly. The results showed that 46% of participants would vote for Biden, and 50% of participants would vote for Trump. There was a MOE or Margin of Error of 4.5%. Because of the way the poll was conducted, I can use these results to generalize to all Latino voters in Florida.
True
The COC Admissions department wants to see how many students would be in favor of using a new program to register for classes. They put a link on their website so that any students that want to try out the program can. The students can then take a survey and say how well they like the new system. This is what method of collecting data was used:
Voluntary responce
Analysis of a random sample of 250 Virginia nurses produced a 95% confidence interval for the mean annual salary of ($42,838 , $49,691). Which is the appropriate conclusion?
We are 95% confident that the interval from $42,838 to $49,691 contains the true mean salary of all Virginia nurses.
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 randomly selected members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Were the A --> Assumptions met
Yes
Dem Now 50% Jan 49% Rep Now 40% Jan 43% The above picture shows the results of a survey in March 2018. The survey results showed that 50% of the survey felt that Democrats should control congress, while 40% felt that Republicans should control congress. Both have a Margin of Error of 2.95%. Is there a statistically significant difference between the proportion in March 2018 who believe that Democrats should control congress and the proportion who believe that Republicans should? Why or why not?
Yes, since there is not an overlap between the two confidence intervals, a larger proportion of the population thought that Democrats should control
When constructing a confidence interval for a sample proportion, you should use which distribution?
z-distribution
Suppose that in sampling for the population proportion, it is found that 20 out of 100 items are defective. Construct a 95% confidence interval for the proportion of defective items in the population.
[0.1216, 0.2784]
In a department store, it is found that out of a randomly selected 64 customers, 21 buy cards. Construct a 95% confidence interval for the proportion of customers buying cards.
[0.2131, 0.4432]
A study was conducted to evaluate the stress level of senior business students at a particular college. Forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). For the forty students, the mean EMG (electromyogram) activity was found to be 35.8 microvolts. In addition, the standard deviation of the EMG readings was found to be 2.5 microvolt. What would be the 99% confidence interval on the true mean EMG activity for all seniors in the class?
[34.7296, 36.8704]
The sampling distribution of a statistic is
the distribution of values taken by a statistic in all possible samples of the same size from the same population.
Brad flips a coin 10 times and records the proportion of heads obtained. He repeats the process of flipping the coin 10 times and records the proportion of heads obtained many, many times. When done, he makes a histogram of the results. This histogram represents
the sampling distribution of the proportion of heads in 10 flips of the coin.
The variability of a statistic is described by
the spread of its sampling distribution.
When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50.
true
A recent survey by the alumni of a major university indicated that the averagesalary of 10,000 of its 300,000 graduates was $125,000. What variable would $125,000 be?
x-bar
A recent survey by the alumni of a major university indicated that the averagesalary of 10,000 of its 300,000 graduates was $125,000. What variable would 10,000 be?
𝑛, n
A survey of 1353 American households found that 18% of the households own acomputer. What variable should be used for the 1353?
𝑛, n
The average late fee for 360 credit card holders was found to be $56.75. What variable would the 360 be?
𝑛, n
In elementary school children, 28% of children are classified as obese. What variable would be used for 28%, or 0.28?
𝑝, p
A survey of 1353 American households found that 18% of the households own acomputer. What variable should be used for the 18%, or 0.18?
𝑝̂ , p-hat
The average salary of all assembly-line employees at a certain car manufacturer is$33,000. What variable would the $33,000 be?
𝜇, mu
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. What is the correct Parameter?
𝜇= the true mean number of days per week that Americans who are members of a fitness club go to their fitness center