Stat 210 Final Study Guide Part 1
Which of the following would be the correct confidence interval?
(.473, .607)
Describe completely the sampling distribution of x bar, the resulting mean amount of time spent studying for this sample of 72 students.
(41.3, 0.801).
A random sample of 12 VCU students was chosen and the number of academic credits each is taking this semester and the number of hours of paid work each does each week was determined. The data is given in the table below. Number of credits Hours paid work 15 18 12 14 7 40 16 12 18 0 15 10 12 20 3 36 19 4 18 6 10 30 11 26
-0.93
The weight of a leatherback turtle is normally distributed with mean 760 pounds and standard deviation 98 pounds. So X ~ N(760, 98). What is the probability that a leatherback turtle will weigh more than 1000 pounds?
.0072
The weight of a leatherback turtle is normally distributed with mean 760 pounds and standard deviation 98 pounds. So X ~ N(760, 98). What is the probability that a leatherback turtle will weigh less than 700 pounds?
.2702
The weight of a leatherback turtle is normally distributed with mean 760 pounds and standard deviation 98 pounds. So X ~ N(760, 98). What is the probability that a leatherback turtle will weigh between 720 pounds and 840 pounds?
.4513
What is the probability that a t-value with 28 degrees of freedom will take a value of 2.048 or less?
.975
The weight of a leatherback turtle is normally distributed with mean 760 pounds and standard deviation 98 pounds. So X ~ N(760, 98). What is the probability that a leatherback turtle will weigh exactly 800 pounds?
0
What is the value of the mean for a standard normal distribution?
0
A random sample of 12 VCU students was chosen and the number of academic credits each is taking this semester and the number of hours of paid work each does each week was determined. The data is given in the table below. Number of credits Hours paid work 15 18 12 14 7 40 16 12 18 0 15 10 12 20 3 36 19 4 18 6 10 30 11 26 What is the value of the coefficient of determination R2?
0.868
What is the value of the standard deviation for a standard normal distribution?
1
A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 63 26 47 48 12 72 52 31 55 126 66 35 22 44 32 37 Calculate the range of the data.
114
A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 63 26 47 48 12 72 52 31 55 126 66 35 22 44 32 37 Calculate the standard deviation of the data.
26.56
What is the mean of the sampling distribution?
2631
Of interest is to estimate the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. For this problem only, assume that the standard deviation of the ages of all such students is 3.3 years. What is the minimum number of graduate students that would need to be selected for the sample to allow the calculation of a 98% confidence interval with margin of error no larger than 1.5?
27
A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 63 26 47 48 12 72 52 31 55 126 66 35 22 44 32 37 Calculate the interquartile range of the data.
27.5
A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 63 26 47 48 12 72 52 31 55 126 66 35 22 44 32 37 Calculate the median of the data.
45.5
A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 63 26 47 48 12 72 52 31 55 126 66 35 22 44 32 37 Calculate the mean of the data.
48
The regression line that gives the linear relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week is predicted number of paid hours = 50.24 - 2.48(number of academic credits). Suppose Nuria is taking 17 academic credits this semester. Use the regression line to predict the number of hours of paid work a student will do if she is enrolled in 17 academic credits.
8.08
A variable X has a normal distribution with mean 54 and standard deviation 5. Approximately what percentage of the observations will fall between 44 and 64?
95%
March Madness commonly refers to the NCAA Men's Division I Basketball Tournament. Many people enjoy March Madness by watching games on television and filling in the ESPN 2019 Tournament Bracket. When you complete a tournament bracket you attempt to correctly pick the winner of all 63 tournament games before the tournament begins, including the eventual national champion. Of interest is to determine the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four. Based on this, what is the population of interest?
All people who completed the ESPN 2019 Tournament Bracket.
March Madness commonly refers to the NCAA Men's Division I Basketball Tournament. Many people enjoy March Madness by watching games on television and filling in the ESPN 2019 Tournament Bracket. When you complete a tournament bracket you attempt to correctly pick the winner of all 63 tournament games before the tournament begins, including the eventual national champion. Of interest is to determine the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four. Based on this, what is the population of interest?
All people who completed the ESPN 2019 Tournament Bracket.
If the confidence level were decreased from 95% to 90%, what impact would this have on the margin of error and width of the confidence interval?
Both the margin of error and the width would decrease.
If the confidence level were decreased from 99% to 90%, what impact would this have on the margin of error and width of the confidence interval?
Both the margin of error and the width would decrease.
In question 2 a 90% confidence interval was computed based on a sample of 150 people who completed the ESPN 2019 Tournament Bracket. If the confidence level were increased to 95%, what impact would this have on the margin of error and width of the confidence interval?
Both the margin of error and the width would increase.
When making inferences on means, what do we do when the population standard deviations are not known?
Calculate the sample standard deviations and use the t-distribution instead of the Z-distribution
As they board, passengers are asked if they live in the City of Richmond, Henrico County, Chesterfield County, Hanover County, or another location (5 options). The location in which a GRTC Pulse passenger lives is what type of characteristic?
Categorical variable
For a quantitative variable, when describing a distribution what things must you describe?
Center, spread, shape and unusual features
To describe a distribution what things must you mention?
Center, spread, shape and unusual features
When describing a distribution, which of the following things must you describe?
Center, spread, shape and unusual features
In partnership with the U.S. Department of Transportation, the Commonwealth of Virginia, the City of Richmond and Henrico County, GRTC and the Project Team launched the GRTC Pulse service on Sunday, June 24, 2018. What type of characteristic is the day GRTC Pulse service was launched
Constant
For all passengers who have ridden the GRTC Pulse since service was launched, of interest is to determine the mean age of all the passengers. What type of characteristic is the mean age of all passengers who have ridden the GRTC Pulse?
Continuous quantitative variable
Suppose that every day the proportion of all passengers on the GRTC Pulse that are either students or employees of VCU is determined. Based on this, the proportion of daily passengers on the GRTC Pulse who are either students or employees of VCU is what type of characteristic?
Continuous quantitative variable
An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described, is this an example of a controlled experiment or an observational study?
Controlled experiment
When describing the relationship between two variables, what things must you describe?
Direction, form and strength
For each GRTC Pulse, the number of stops it makes per day are counted. What type of characteristic is the number of stops for each GRTC Pulse?
Discrete quantitative variable
What type of characteristic is "number of enrolled students in a class"?
Discrete quantitative variable
True or false: a stem-and-leaf plot and a histogram are graphical methods for displaying qualitative data.
False
True or false: with two categorical variables we describe the relationship between the two variables by describing the direction, form, and strength of the relationship.
False
It is conjectured that the proportion of all hares and rabbits found in Europe that are European hares is 0.60. Since European hares are larger than rabbits with longer legs, they are faster and can escape predators more easily. Therefore, the belief is that the proportion of all hares and rabbits found in Europe that are European hares is actually greater than 0.60. State the appropriate null and alternative hypotheses that should be tested.
H0: = .60 versus HA: < .60
The two most recent tests in STAT 210 have been tests 5 and 6. Suppose population 1 consists of all students who took both tests and who picked up test 5 from their instructor prior to test 6, while population 2 consists of all students who took both tests but did not pick up test 5 from their instructor prior to test 6. It is conjectured that the mean score on test 6 for all students who picked up test 5 is greater than the mean score on test 6 for all students who did not pick up test 5. State the appropriate null and alternative hypotheses that should be tested. Correct answer:
H0: µ1= µ2 Ha: µ1>µ2
Many graduate programs require students to pass a comprehensive exam (or qualifying exam, or something equivalent) before being admitted into candidacy to receive the degree. Suppose the population consists of all comprehensive exams (or equivalent) that are given to students in graduate programs, and of interest is the mean number of questions asked on the comprehensive exams. It is conjectured that the mean number of questions asked on all comprehensive exams is 8, and of interest is to test this conjecture versus the alternative that the mean number of questions asked on all comprehensive exams is different from 8. State the appropriate null and alternative hypotheses that should be tested.
H0: μμ = 8 versus Ha: μμ ≠ 8
Is the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four in the confidence interval computed in question 2?
I don't know
Which of the following statements is true?
If possible, we want to make the probability of making a type I error as small as possible and make the probability of making a type II error as small as possible.
The regression line that gives the linear relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week is predicted number of paid hours = 50.24 - 2.48(number of academic credits). Which of the following is the correct interpretation of the slope of this regression line?
If the number of academic credits increases by 1 credit, then the predicted number of paid hours of work decreases by 2.48 hours.
The regression line that gives the linear relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week is predicted number of paid hours = 50.24 - 2.48(number of academic credits). Which of the following is the correct interpretation of the intercept of this regression line?
If the number of academic credits is 0 credits, then the predicted number of paid hours of work is 50.24 hours.
The branch of statistics that involves using statistics computed from sample data to make statements about unknown population parameters is which of the following?
Inferential statistics
Which of the following is a measure of spread that is resistant to outliers?
Interquartile Range
Which of the following statistics is a measure of spread that would be resistant to outliers?
Interquartile Range
Suppose the shape of a stem-and-leaf plot is skewed right. What is the best measure to describe the spread?
Interquartile range
It is believed that older students typically have to work more hours to support themselves (and possibly a family) than younger students. Hence the age of the student affects the relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week. In this scenario, the age of the student is which of the following?
Lurking variable
Which of the following is a measure of center that would be heavily influenced by outliers?
Mean
Suppose the shape of a stem-and-leaf plot is skewed right. What is the best measure to describe the center?
Median
Which of the following is a measure of center that is resistant to outliers?
Median
A random sample of 85 graduate level classes was selected and the number of enrolled students during the Fall 2017 semester was recorded for each. The data is displayed in the boxplot below. Use this boxplot to completely describe the center of the distribution of the number of enrolled students in this sample of 85 graduate level classes.
Median = 17.5
A sample of 300 passengers who have ridden the GRTC Pulse since service was launched was selected in the following manner. There are a total of 14 GRTC Pulse stations. A random sample of 5 of the 14 GRTC Pulse stations was selected. Then for each of these 5 GRTC Pulse stations (but not the other 9), a random sample of 60 passengers who boarded from that station was selected. What type of sampling procedure is this an example of?
Multistage random sampling
Used car auctions give car dealers an opportunity to increase their used car inventory by purchasing cars used as rental cars, assigned to company executives, and other similar activities. Suppose population 1 is all black cars sold at used car auctions, and population 2 is all white cars sold at used car auctions. Of interest is to estimate the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions. To estimate the parameter the following was done. A group of 12 black sports cars being sold at used car auctions was selected. The distribution of the costs of these cars is heavily skewed to the right, with a mean of $125,310 and a standard deviation of $42,255. A group of 24 white compact cars being sold at used car auctions was selected. The distribution of the costs of these cars is fairly symmetric, with a mean of $18,225 and a standard deviation of $6,395. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions. Do we have independent simple random samples?
No
Are the populations normal or the sample sizes large enough for the Central Limit Theorem to apply?
No, because the first population was heavily skewed, but the sample size of 12 is too small for the CLT to apply (the sample size must be greater than or equal to 40 if the population is heavily skewed). Central Limit Theorem does not apply.
The population of interest is all VCU employees and the parameter of interest is the proportion of all VCU employees who use the GRTC Pulse service. Suppose a sample of 100 VCU employees were randomly selected and contacted, but only 50 of them responded and answered the questions. If the characteristics of those who did respond and those who did not respond are different, what type of bias would this create?
Nonresponse bias
On their website GRTC Pulse lists five different time periods: AM Peak (6:00-9:00 AM), Midday (9:00 AM - 4:00 PM), PM Peak (4:00 - 7:00 PM), Off Peak (7:00 - 11:30 PM), and Late Night (11:30 PM - 6:00 AM). Of interest is to determine which of these five time periods has the highest passenger satisfaction rating. Hence a study was conducted, as follows. A sample of 40 passengers from each time period was selected (40*5 = 200 total passengers), and as they exited the GRTC Pulse they were asked to complete a very short satisfaction survey. The survey results for the passengers in each group were averaged, then the five averages were compared to determine which time period had the highest passenger satisfaction rating. As described, is this an example of a controlled experiment or an observational study?
Observational study
An observation that falls within the range of the other X values but which lies far above or below the regression line and hence produces a large residual is which of the following?
Outlier
Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. As reported by the department of tourism, the total number of visitors in 2019 was 120,000. In this scenario, is 120,000 an example of a parameter or a statistic?
Parameter
Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on a brochure published by the resort, the proportion of tourists who visit the Bahamas and spent time at Atlantis Paradise Island is .20. A statement about a population parameter, such as π=.20 is which of the following?
Parameter?
Which of the following is a graphical method of displaying qualitative or categorical variables?
Pie chart
What type of sample do we usually prefer?
Random sample
An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described in the example what is the response variable?
Rating of the quality of ravioli
Suppose a test is conducted with a p-value = .0340 and α = .05. What decision should we make?
Reject the null hypothesis
p-value = .000095950879 and α = .10. What decision should we make?
Reject the null hypothesis
If both populations are known to be normal, what size samples are required to complete the inference procedures?
Sample sizes do not matter
Which of the following is a graphical method that is used to describe the relationship between two quantitative variables?
Scatterplot
For all passengers who have ridden the GRTC Pulse since service was launched, of interest is to determine the mean age of all the passengers. Suppose a sample of 20 passengers who have ridden the GRTC Pulse since service was launched was selected. The sample is purposely selected such that all 20 passengers were employed by VCU; passengers employed by other agencies and companies are excluded from the sample. In this scenario, what type of bias could this cause?
Selection bias
The p-value is .0925. What is the correct decision at the α = .10 level of significance?
Since p-value < .10 we reject the null hypothesis
The main entrees at Chick-fil-A can be grouped into three categories: sandwiches (to include Chick-fil-A Chicken Sandwich, Chick-fil-A Deluxe Sandwich, Spicy Chicken Sandwich, Spicy Deluxe Sandwich, Grilled Chicken Sandwich, and Grilled Chicken Club Sandwich), nuggets/strips (to include Chick-fil-A Nuggets, Chick-n-Strips, and Grilled Nuggets) and wrap (Grilled Chicken Cool Wrap). The Chick-fil-A restaurants are also classified by location, such as Mall, Urban/Downtown, or Suburban. Of interest is to determine if there is a relationship between the category of entrée chosen and the restaurant location. A random sample of 450 orders was analyzed, and the following chart presents the conditional distributions of the category of entrée for each restaurant location. Which of the following is true?
Since the conditional distributions are similar, there is not an association between the category of entrée chosen and the restaurant location.
When describing a distribution, which of the following do you not use?
Size
A random sample of 85 graduate level classes was selected and the number of enrolled students during the Fall 2017 semester was recorded for each. The data is displayed in the boxplot below. Use this boxplot to describe the shape of the distribution of the number of enrolled students in this sample of 85 graduate level classes.
Skewed left
When income/salaries of a collection of people are graphed, the distribution usually has a very long tail to the right because there are a few people who make LOTS of money while most others earn much less. What type of distribution does this describe?
Skewed right
Which of the following is a measure of spread that is influenced by outliers?
Standard Deviation
A sample of 400 visitors to the Bahamas in 2019 were selected and each was asked whether they spent some time at Atlantis Paradise Island. In this sample, 120 visitors, or 30%, indicated that they spent some time at Atlantis Paradise Island. In this scenario, is 30% an example of a parameter or a statistic?
Statistic
Suppose a sample of 35 passengers who have ridden the GRTC Pulse since service was launched is selected, as follows. As they board, passengers are asked if they live in the City of Richmond, Henrico County, Chesterfield County, Hanover County, or another location (5 options). A random sample of 7 passengers who have ridden the GRTC Pulse since service was launched was randomly chosen from each of the 5 locations. What type of sampling procedure is this an example of?
Stratified random sampling
This is a concept/definition question: which of the following sampling methods would give the highest likelihood of getting a sample of GRTC Pulse passengers that is representative of all GRTC Pulse passengers in the population?
Stratified random sampling
Since the population standard deviation is unknown, the test statistic is......
T = -1.703
Which of the following is a correct statement?
The IQR is a measure of spread around the median.
An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described in the example, what is the treatment?
The method of preparing ravioli
Used car auctions give car dealers an opportunity to increase their used car inventory by purchasing cars used as rental cars, assigned to company executives, and other similar activities. Suppose population 1 is all black cars sold at used car auctions, and population 2 is all white cars sold at used car auctions. Of interest is to estimate the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions. Based on this, using both the appropriate symbol and in words, state the one parameter of interest.
The parameter of interest is µ1-µ2, the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions.
Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on this information, what is the parameter of interest?
The proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island
Using both the appropriate symbol and in words, what is the parameter of interest?
The proportion ππ of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four.
Choose the appropriate conclusion sentence based on your decision in question 4.
There is insufficient evidence that the proportion of all hares and rabbits found in Europe that are European hares is greater than .60.
Choose the appropriate conclusion.
There is sufficient evidence that the mean number of questions asked on all comprehensive exams is different from 8.
What of the following is not a correct comparison among the Z-distribution and all the t-distributions?
They have the same standard deviation.
A student computes the correlation coefficient to be r = +1.32. What does this value tell you?
This student either doesn't know what they are doing or made a calculation error (or both).
Of interest is to study the relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week. Specifically, of interest is to use the number of academic credits the student is taking to predict the number of hours of paid work the student does each week. Based on the information above, which of the following is the correct identification of the independent variable X and the dependent variable Y?
This student either doesn't know what they are doing or made a calculation error (or both).
True or false: With two categorical variables we cannot describe the direction, form and strength of the relationship. Instead we should create a two-way table, a marginal distribution, and then conditional distributions, and compare the conditional distributions to determine if there is a relationship between the two variables or not.
True
With stratified random sampling you select at least one subject from every group, while in multistage random sampling you first select some groups and hence subjects are not selected form every group?
True
Is the population standard deviation known or unknown?
Unknown
Consider the information provided to the left and the hypotheses specified in question 1. A simple random sample of 81 comprehensive exams was selected and the number of questions asked on each comprehensive exam in the sample was recorded. The mean number of questions asked for this sample of 81 comprehensive exams was 7.3 with a standard deviation of 3.7. The distribution of the data was bimodal and slightly skewed to the left. We want to use this information to test the hypotheses stated in question 1 at the α = .10 level of significance. Are the assumptions met?
We had a simple random sample, and the sample size is large enough for the Central Limit Theorem to apply (n = 81 > 15). Therefore, the assumptions are satisfied.
Choose the correct interpretation of the confidence interval in question 2.
We have 90% confidence that the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four is between .473 and .607.
Choose the correct interpretation of the confidence interval.
We have 98% confidence that the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams is between 26.22 and 28.78 years old.
The 99% confidence interval for the mean IQ of all students at this university is (98.8, 108.8). Which of the following is the correct interpretation of this interval?
We have 99% confidence that the mean IQ of all students at this university is between 98.8 and 108.8
A simple random sample of 80 hares and rabbits found in Europe is selected, and 54 of these 80 hares and rabbits are European hares. State the two assumptions that must be satisfied in order to complete this hypothesis test, and determine whether they are satisfied or not in this situation.
We have a simple random sample, and both nπ0 = 80(.60) = 48 and n(1-π0) = 80(1 - .60) = 32 are > 10, so we do have a large enough sample size for the Central Limit Theorem to apply.
In 2018, 63.5% of people who completed the ESPN 2018 Tournament Bracket had their choice to become the national champion make the Final Four. If a simple random sample of 125 people who completed the ESPN 2018 Tournament Bracket was selected and the proportion who had their choice to become the national champion make the Final Four was determined, describe completely the sampling distribution of the sample proportion p̂. What are the two assumptions required in order to describe the sampling distribution, and are they met?
We have a simple random sample, and since nπ = 125(.635) = 79.375 and n(1-π) = 125(1 - .635) = 45.625 are both greater than 10, the sample size is large enough for the CLT to apply.
In 2018, 63.5% of people who completed the ESPN 2018 Tournament Bracket had their choice to become the national champion make the Final Four. If a simple random sample of 125 people who completed the ESPN 2018 Tournament Bracket was selected and the proportion who had their choice to become the national champion make the Final Four was determined, describe completely the sampling distribution of the sample proportion p̂. What are the two assumptions required in order to describe the sampling distribution, and are they met?
We have a simple random sample, and since nπ = 125(.635) = 79.375 and n(1-π) = 125(1 - .635) = 45.625 are both greater than 10, the sample size is large enough for the CLT to apply.
Of interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. A simple random sample of 31 students enrolled in graduate programs was selected, and the age of each student when they took the comprehensive exam was recorded. The mean age at the time of taking the comprehensive exam for this sample of 31 students was 27.5 years with a standard deviation of 2.9 years; there were no outliers in the sample that would lead one to suspect heavy skewness in the distribution. If appropriate, we want to use this information to calculate and interpret a 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. Use this information to answer questions 3 - 5. What are the two assumptions? Are the assumptions satisfied?
We have a simple random sample, and the sample size is large enough for the Central Limit Theorem to apply (n = 31 > 15), so the assumptions are satisfied
Students preparing for comprehensive exams usually spend many hours studying. Suppose it is known that the time students spend studying for comprehensive exams has a distribution that is skewed heavily to the right with a mean of 41.3 hours and a standard deviation of 6.8 hours. If a simple random sample of 72 students is selected and the amount of time each spent studying for the comprehensive exam is determined, we want to determine the sampling distribution of the sample mean. What are the two assumptions, and are they met in this scenario?
We have a simple random sample, and the sample size is large enough to apply the Central Limit Theorem (n = 72 > 40).
March Madness commonly refers to the NCAA Men's Division I Basketball Tournament. Many people enjoy March Madness by watching games on television and filling in the ESPN 2019 Tournament Bracket. When you complete a tournament bracket you attempt to correctly pick the winner of all 63 tournament games before the tournament begins, including the eventual national champion. A simple random sample of 150 people who completed the ESPN 2019 Tournament Bracket was selected, and 81 out of the 150 people who completed the ESPN 2019 Tournament Bracket had their choice to become the national champion make the Final Four. If appropriate, use this information to calculate and interpret a 90% confidence interval for the proportion of all people who completed the ESPN 2019 Tournament Bracket whose choice to become the national champion made the Final Four. What are the two assumptions that are required in order to calculate a confidence interval, and are they met in this situation?
We require a simple random sample, which is met in this case; and we require that both np̂ = 150(.54) = 81 and n(1-p̂) = 150(1 - .54) = 69 are greater than 10, which is met in this case
What is the point estimate of μ1 - μ2?
X-bar1 - Xbar2
Consider the information and hypotheses in question 2. A simple random sample of 63 students who picked up test 5 was selected, and the mean score on test 6 for this sample of students was 85 with a standard deviation of 13.2. An independent simple random sample of 41 students who did not pick up test 5 was selected, and the mean score on test 6 for this sample of students was 72 with a standard deviation of 18.2. Both distributions are skewed heavily to the left. If appropriate, use this information to test the hypotheses stated in question 2 at the α = .10 level of significance. Use this information to answer questions 3-5. Do we have two independent simple random samples?
Yes
Are the two populations normal or the two sample sizes large enough for the Central Limit Theorem to apply?
Yes because the sample sizes are large enough for the Central Limit Theorem to apply
What would the value of the test statistic be when testing the hypotheses stated in question 1?
Z = 1.37
Many graduate programs require students to pass a comprehensive exam (or qualifying exam, or something equivalent) before being admitted into candidacy to receive the degree. Of interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. Based on the information provided, what is the population of interest?
all students enrolled in graduate programs that require students to take comprehensive exams.
Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on this information, what is the population of interest?
all visitors to the Bahamas in 2019.
Of interest is to study the relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week. Specifically, of interest is to use the number of academic credits the student is taking to predict the number of hours of paid work the student does each week. Based on the information above, which of the following is the independent variable?
number of academic credits a VCU student is taking
Of interest is to study the relationship between the number of academic credits a VCU student is taking this semester and the number of hours of paid work the student does each week. Specifically, of interest is to use the number of academic credits the student is taking to predict the number of hours of paid work the student does each week. Based on the information above, which of the following is the dependent variable?
number of hours of paid work the student does each week
Choose the correct decision for testing the hypotheses stated in question 1 at the α = .05 level of significance.
p-value = .0855, Since p-value > .05 we fail to reject H0
Which of the following is the point estimate of the population proportion π?
p̂
The sampling distribution can be described as follows
p̂~ N(.635, .043).
Which of the following values represents the strongest correlation between two variables?
r = -0.92
True or false: with quantitative variables, to completely describe the relationship between the two variables it is recommended to construct a scatterplot to graphically display the relationship and compute the correlation coefficient to numerically describe the relationship
true
What is the point estimate of the population mean μ?
x bar
Are the sample sizes large enough for the Central Limit Theorem to apply?
yes
Suppose population 1 is all blue cars sold at used car auctions, and the mean sale price of all such blue cars is $24,579 with a standard deviation of $3,691. Additionally suppose population 2 is all red cars sold at used car auctions, and the mean sale price of all such red cars is $21,948 with a standard deviation of $4,028. If a simple random sample of 47 blue cars sold at used car auctions is selected and xbar1= the mean sale price of the 47 blue cars in the sample is determined, and if an independent simple random sample of 59 red cars sold at used car auctions is selected and xbar2= the mean sale price of the 59 red cars in the sample is determined, if appropriate describe completely the sampling distribution of xbar1-xbar2. Do we have two independent simple random samples?
yes
Consider the statement to the left. Based on this, using both the appropriate symbol and in words, what is the parameter of interest?
µ = the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams.
