Elementary Statistics Exam 3
In June 2017, a survey was conducted in which a random sample of 1474 U.S. adults was asked the following question: "In 1973 the Roe versus Wade decision established a woman's constitutional right to an abortion, at least in the first three months of pregnancy. Would you like to see the Supreme Court completely overturn its Roe versus Wade decision, or not?" The results were: Yes—28%, No—64%, Unsure—8% Which of the following is true about this scenario?
8%, 64%, and 8% are all statistics.
Suppose the scores on an exam are normally distributed with a mean μ = 75 points and standard deviation σ = 8 points. What is the exam score for an exam whose z-score is 1.25?
85
Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points. Suppose that the top 4% of the exams will be given an A+. In order to be given an A+, an exam must earn at least what score? Report your answer in whole numbers.
89
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 20 students from this distribution. What is the probability that a SRS of 20 students will spend an average of between 600 and 700 dollars? Round to five decimal places
=0.93759
Which of the following best describes the sampling distribution of a statistic?
A distribution of a single statistic from repeated random samples of the same size, from the same population.
When the population is not normally distributed, the sampling distribution of the mean approximates which of the following?
A normal distribution given a large enough sample
The run times of a marathon runner are approximately normally distributed. The z-score for his run this week is - 2 . Which one of the following statements is a correct interpretation of his z-score? This week his time was 2 ___ ___ than his ___
standard deviations, lower, average time
The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The Central Limit Theorem says that
the average burnout time of a large number of bulbs has a distribution that is close to Normal.
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^p denote the proportion in the sample who say they support the increase. Suppose that 67% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
0.0121
Suppose that 75% of all dialysis patients will survive for at least 5 years. In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
0.12411
The following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones: Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the Standard Deviation Rule, how likely is it that a randomly chosen battery lasts longer than 10.4 hours?
0.16
The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. Suppose a golfer played the course today. Find the probability that her score is at least 74.
0.3694
A factory produces plate glass with a mean thickness of 4mm and a standard deviation of 1.1mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 4.06 mm?
0.70728
According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was 28.08 with a standard deviation of 1.97. Jeronica is a social worker with an hourly wage of 31.60. What is Jeronica's z-score? (Round your answer to 2 decimal places)
1.79
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .2005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval? Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean? Round answers to four decimal places.
15.8495, 16.2505
Pictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 30. Based on the histograms, what is the most likely value of the population mean?
3.0
In June 2017, a survey was conducted in which a random sample of 1484 U.S. adults was asked the following question: "In 1973 the Roe versus Wade decision established a woman's constitutional right to an abortion, at least in the first three months of pregnancy. Would you like to see the Supreme Court completely overturn its Roe versus Wade decision, or not?" The results were: Yes—30%, No—67%, Unsure—3% Which of the following is true about this scenario?
30%, 67%, and 3% are all statistics
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct?
40% is a statistic
The weights of cockroaches living in a typical college dormitory are approximately distributed with a mean of 80 grams and a standard deviation of 4 grams. The percentage of cockroaches weighing between 77 grams and 83 grams is about ___ %. Round to the nearest whole number.
55%
In June 2015, Gallup conducted a poll of a random sample of 15322 adults to determine the well-being of people living in the United States. One question asked, "Did you exercise at least 30 minutes for 3 or more days in the past week?" In the survey, 56.3% of males and 43.7% of females responded yes to this question. Which of the following is true about this scenario?
56.3 and 43.7 are both statistics
In June 2015, Gallup conducted a poll of a random sample of 14712 adults to determine the well-being of people living in the United States. One question asked, "Did you exercise at least 30 minutes for 3 or more days in the past week?" In the survey, 58.3% of males and 41.7% of females responded yes to this question. Which of the following is true about this scenario?
58.3% and 41.7% are both statistics.
Pictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 40. Based on the histograms, what is the most likely value of the population mean?
8
Which of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply.
( all of them ) The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough., The distribution is normal regardless of the sample size, as long as the population distribution is normal., The distribution's mean is the same as the population mean., The distribution's standard deviation is smaller than the population standard deviation.
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years. Round your answer to three decimal places.
(0.163, 0.189)
The number of days (X) after mailout it takes a utility company to receive payment for a customer's bill is a normal random variable with a mean of 31 days and a standard deviation of 6 days The probability is 0.997 and that bill will be received between which of the following number of days?
(13,49)
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule. (a) What proportion of the students scored at least 27 points on this test, rounded to five decimal places? (b) What is the 63 percentile of the distribution of test scores, rounded to three decimal places?
(a) = 0.00621, (b) = 22.664
A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 1.50 days with an approximately normal distribution. (a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.
(a) = 0.12348, (b) = 0.81947
The Environmental Protection agency requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individually trucks according to a Normal distribution with mean 1.45 grams per mile driven and standard deviation 0.40 grams per mile. (a) What is the 66th percentile for NOX exhaust, rounded to four decimal places? b) Find the interquartile range for the distribution of NOX levels in the exhaust of trucks rounded to four decimal places.
(a) = 1.6150, (b) = 0.5396
A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people. If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
Different sample proportions, ^p, would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion, p.
uppose two students from Georgia State University, working as interns for the American National Elections Studies agency (ANES), are both assigned to survey a random sample of registered voters and ask whether or not they will vote for a certain candidate. The first intern plans to select 500 voters and the second intern plans to select 1500 voters. If each intern conducted the study repeatedly (selecting different samples of people each time ... but using the same sample size), which one of the following would be true regarding the resulting sample proportion, ^p, of "yes" responses for each intern?
Different sample proportions, ^p, would result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, p.
The following displays two normal distributions. Which of the following are true? I. The mean of A is less than the mean of B. II. The standard deviation of A is less than B. III. The area under the curve of A is less than B.
I and II only
Suppose that a candy company makes a candy bar whose weight is supposed to be 50 grams, but in fact, the weight varies from bar to bar according to a normal distribution with mean μ = 50 grams and standard deviation σ = 2 grams. If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?
It is extremely unlikely for this to occur; the probability is very close to 0.
Left-handedness occurs in about 12% of all Americans. Males are slightly more likely than females to be left-handed, with 13% of males and 11% of females being left-handed. Suppose a random sample of 80 females and 100 males is chosen. Let X be the number of males (out of the 100) who are left-handed. Let Y be the number of females (out of the 80) who are left-handed. Let Z be the total number of left-handed individuals in the sample (males and females together). Which of the following is true regarding the random variables X and Y?
Only X can be well approximated by a normal random variable.
Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply.
The distribution will be normal as long as the population distribution is normal., The distribution's mean is the same as the population mean 60.
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
We take repeated random samples of size 15 from a population that is normally distributed., We take repeated random samples of size 50 from a population of unknown shape.
Parking survey: For a class assignment, a group of statistics students set up a table near the student parking lot. They asked students who passed by to complete a quick survey about whether they support the building of a multi-level parking structure that would add 425 new spaces at the college. They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population does the confidence interval apply?
The results do not apply to any population because this was a convenience sample.
An interactive poll on the front page of the CNN website in October 2011 asked if readers would consider voting for Herman Cain, who at the time, was a Republican presidential candidate. A statistics student used the information from the poll to calculate the 95% confidence interval. He got (0.53,0.59). He also conducted a hypothesis test. He found very strong evidence that more than half of voters would consider voting for Herman Cain. To what population do these conclusions apply?
The results do not apply to any population because this was a voluntary response sample.
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus?
The sample needs to be random but we don't know if it is., The actual count of those who do not drive to campus is too small., n(1−^p) is not greater than 10.
Concert marketing: GSU's Rialto Center for the Performing Arts wanted to investigate why ticket sales for the upcoming season significantly decreased from last year's sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail. Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail?
The sample needs to be random, but we don't know if it is., The actual count of community residents who received the concert brochure by mail is too small., n^p is not greater than 10.
Suppose the American National Elections Studies agency (ANES) wishes to conduct a survey. It plans to ask a yes/no question to determine if those surveyed plan to vote for a certain candidate. One proposal is to randomly select 400 people and another proposal is to randomly select 1600 people. Which of the following is true regarding the sample proportion ^p of "yes" responses?
The sample proportion from sample of 1,600 is more likely to be close to the true population proportion, p.
A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people. Which of the following is true regarding the sample proportion, ^p, of "yes" responses?
The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p.
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct?
The sampling distribution of the proportion of damaged trees is approximately Normal
A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people. Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, ^p, of "yes" responses?
The standard deviation of the sampling distribution will be 3 times larger with sample size 100.
Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 grams. If the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised?
There is about a 2.5% chance of this occurring.
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion, ^p, to be within 0.04 of the true proportion, p (i.e., between 0.16 and 0.24)? (Hint: Use the sampling distribution of the sample proportion in this case.)
There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion.
