STA 296 Chapter 3 Review
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 What is the sample statistic?
(p-hat)= proportion of the sample of 1,017 randomly selected U.S. adult who have "no confidence at all" in the media.
A study of n=2252 adults age 18 or older found that 72% of the cell phone users send and receive text messages. A studyof n=800 teens age 12 to 17 found that 87% of the teen cell phone users send and receive text messages. What is the bestestimate for the difference in the proportion of cell phone users who use text messages, between adults (defined as 18and over) and teens? Give the notation (as a difference with a minus sign) for the quantity that gives the best estimate Let group 1 be the adult cell phone users and let group 2 be the teen cell phone users.
(p-hat1)-(p-hat2)
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" What is the sample statistic?
(x-bar) = the average number of text messages sent or received per day of 755 randomly selected U.S. adults
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" Give appropriate notation and the value of the sample statistic.
(x-bar)=41.5
A study of n=2252 adults age 18 or older found that 72% of the cell phone users send and receive text messages. A study of n=800 teens age 12 to 17 found that 87% of the teen cell phone users send and receive text messages. What is the best estimate for the difference in the proportion of cell phone users who use text messages, between adults (defined as 18and over) and teens? Give the value of the best estimate (point estimate of population parameter)
-0.15
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media
0.184 to 0.236
When 460 junior college students were surveyed,100 said that they have previously owned a motor cycle. Find a point estimate for p, the population proportion of students who have previously owned a motorcycle.
0.217
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 What is the sample being used?
1,017 randomly selected U.S. adults
Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same),indicate which of the three confidence intervals would be the most likely result. Decrease the sample size to n = 40
2.46 to 2.84 (wider)
Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentilesof the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same),indicate which of the three confidence intervals would be the most likely result. Increase the confidence level to 99%
2.46 to 2.84 (wider)
Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same),indicate which of the three confidence intervals would be the most likely result. Increase the number of bootstrap samples to 4,000
2.50 to 2.80 (the same)
Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same),indicate which of the three confidence intervals would be the most likely result. Decrease the confidence level to 90%
2.53 to 2.77 (narrower)
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages, with standard error about 6.1. Find 95% confidence interval estimate for the parameter of interest
29.3 to 53.7
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" Find 95% confidence interval estimate for the parameter of interest
29.3 to 53.7
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" What is the sample being used?
755 randomly selected US cell phone users age 18 and over
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how muchtrust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting thenews fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" ofconfidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we areintrested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 What is the population of interest?
All U.S. adults
Identify if each of the following statements is a proper interpretation of a 95% confidence interval. I am 95% sure that this interval will contain the population parameter.
Correct
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 Is the following statement an appropriate interpretation of this interval? We are 95% sure that the proportion of U.S. adults who have no confidence in the media is between *** and ***(The numbers are the answer from the question above
Correct
Suppose that a student is working on a statistics project using data on pulse rates collected from a random sample of 100 students from her college. She finds a 95% confidence interval for mean pulse rate to be (65.5, 71.8). Interpretation this interval.
I am 95% sure that the mean pulse rate for all students will fall between 65.5 and 71.8 beats per minute.
Identify if each of the following statements is a proper interpretation of a 95% confidence interval. 5% of the population values will fall within this interval.
Incorrect
Identify if each of the following statements is a proper interpretation of a 95% confidence interval. I am 95% sure that this interval will contain the sample statistic.
Incorrect
Identify if each of the following statements is a proper interpretation of a 95% confidence interval. The probability that the population parameter is in this interval is 0.95.
Incorrect
A sample consists of the following values: 84, 70, 79, 91, 87. Which of the following are possible bootstrap samples from this original sample? 79, 87, 70, 84, 79, 91
Not Possible
A sample consists of the following values: 84, 70, 79, 91, 87. Which of the following are possible bootstrap samples from this original sample? 79, 87, 91, 84, 69
Not Possible
A random sample of 500 students shows that 40% of students use the Student learning Center at some point during their time on campus, with a margin of error of 5%. Based on this information, identify each of the following as plausible or not for the percent of the entire student body that use the Student learning Center at some point during their time on campus. Use the information above to answer the question. 52%
Not plausible
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 What is the population parameter of interest, and what is the correct notation for this parameter?
P = proportion of U.S. adults who have "no confidence at all" in the media.
State whether the quantity described is a parameter or a statistic and give the correct notation. Give the value of the quantity described: Average enrollment in charter schools in Illinois. In 2014, there were 148 charter schools in the state of Illinois and the total number of students attending the charter schools was 59,388
Parameter, μ =401.3
A random sample of 500 students shows that 40% of students use the Student learning Center at some point during their time on campus, with a margin of error of 5%. Based on this information, identify each of the following as plausible or not for the percent of the entire student body that use the Student learning Center at some point during their time on campus. Use the information above to answer the question. 38%
Plausible
A sample consists of the following values: 84, 70, 79, 91, 87. Which of the following are possible bootstrap samples from this original sample? 87, 84, 79, 70,79
Possible
Choose the one alternative that best completes the statement or answers the question. Which formula do we use to find a 95% CI using the standard error (SE)?
Statistic ±2×SE
Choose the one alternative that best completes the statement or answers the question. Which formula do we use to find a 95% CI using the Margin of error (ME)?
Statistic ±ME
What value should be recorded for each bootstrap sample?
The bootstrap statistic
If samples of size n = 90 had been used instead of n = 30, which of the following would be true ?
The sample mean would have less variability
If samples of size n = 20 had been used instead of n = 30, which of the following would be true ?
The sample mean would have more variability
If samples of size n = 90 had been used instead of n = 30, which of the following would be true ?
The sample means would be centered at the same value.
Where should the bootstrap distribution be centered?
The sample statistic
How do you estimate the standard error from the bootstrap distribution?
Use the standard deviation from the bootstrap distribution
Data collected by child development scientists produced the following 90% confidence interval for the average age (in months) at which children say their first word: 10.4 < μ < 13.8.
We are 90% confident that the mean age at which children say their first word is between 10.4 and 13.8 months.
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" Interpret the 95% confidence interval.
We are 95% confident that the average number of text messages sent or received per day for all US cell phone users age 18 and over is between 29.3 and 53.7 .
Suppose a 95% CI for mean commute time of workers in Atlanta is 27.2 to 31.0. Which of the following is the correct interpretation of this confidence interval?
We are 95% sure that the mean commute time for all Atlanta workers is between 27.2 and 31.0 minutes.
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" What is the population of interest?
all US cell phone users age 18 and over
In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all". Suppose we are interested in the proportion of U.S. adults who have "no confidence at all" in the media. The estimate of the standard error is0.013 Suppose the parameter of interest is the proportion of U.S. adults who have "no confidence at all" in the media. give appropriate notation and the value of the sample statistic.
p-hat=.21
A study of n=2252 adults age 18 or older found that 72% of the cell phone users send and receive text messages. A study of n=800 teens age 12 to 17 found that 87% of the teen cell phone users send and receive text messages. What is the best estimate for the difference in the proportion of cell phone users who use text messages, between adults (defined as 18and over) and teens? Give the notation (as a difference with a minus sign) for the quantity we are trying to estimate. Let group 1 be the adult cell phone users and let group 2 be the teen cell phone users.
p1 - p2
State whether the quantity described is a parameter or a statistic and give the correct notation. Give the value of the quantity described: Proportion of US adults who own a cell phone. In a survey of 1006 US adults in 2014, 90% said they had a cell phone.
statistic , p ^ (p-hat) = 0.90
If X1, X2, X3, ..., XN are the N observations of a variable from a population, then the population mean is symbolized by
μ
A random sample of n=755 US cell phone users age 18 and older in May 2011 found that the average number of text messages sent or received per day is 41.5 messages. They also report that at 95% confidence level, the "margin of sampling error is12.2" What is the population parameter of interest, and what is the correct notation for this parameter?
μ = the average number of text messages sent or received per day for all US cell phone users age 18 and over
