Statistitcs
Looking at the following boxplot, what percentage of data falls between 1 and 5?
75%
What is the factor in this experiment?
Caffeine or placebo intake
A group of boys believe that there is a relationship between the act of sending flowers to a girl and texts received as a result. A study was carried out in which a sample of girls were asked whether they received any flowers and how many texts they sent in response. What type of variable is the explanatory variable?
Categorical
Which graph is used to display quantitative data?
Dot Plot
If we set α = 0.05, what can we do to increase power?
Increase sample size.
Medical experiments are often double blind in nature. What does this mean?
Neither the subject nor the person evaluating the subject (the doctor or nurse) knows which treatment the subject receives
What will be the shape of the sampling distribution of x̄ if all samples of size 20 were taken?
Normal
With a p-value of 0.287, what is the appropriate conclusions to make?
Our data does not provide strong enough evidence for rejecting H0
What is the approximate shape of the data?
Right-skewed
What type of visual display should be used to summarize this data?
Side-by-side boxplots
Which of the following statements is true about the standard deviation?
Standard deviation has the same units as data.
The data in question is given here in the following table. Which stemplot should we examine for outliers and strong skewness?
Stemplot of differences between reference and generic drug absorptions (PLOT B)
A student in Stat 121 wants to estimate the mean score on the Stat 121 final exam from last semester. They asked 200 students who took the class last semester what their final exam score was and recorded it. What is the sample?
The 200 students interviewed
Researchers for the National Institute of Child Health and Human Development studied 208 infants whose brains were temporarily deprived of oxygen as a result of complications at birth. These babies were subjects in an experiment to determine if reducing body temperature for three days after birth improved their chances of surviving without brain damage. What is the sample?
The 208 babies who were a part of this experiment
What is the explanatory variable in this study?
The type of general mathematics instruction received
What is the correct description of the median of a distribution that is described by a density curve?
The value that divides the area of the density curve in half
Given the following data and five number summary, determine the value of suspected outliers. Data: 16, 4, 20, 6, 13, 19, 7, 22, 8, 30 Five number summary: 4, 7, 14.5, 20, 30
There are no outliers in this data set.
Suppose the actual p-value for a two-sided test is 0.140. On the basis of this p-value, what should you conclude at α = 0.05?
There is insufficient evidence to conclude that the mean difference between the absorption rate of the reference drug and the absorption rate of the generic drug is not equal to zero
True or False: Increasing the sample size will lead to a smaller margin of error.
True
True or False: When the population standard deviation is unknown, we use t* rather than z* and s rather than σ.
True
Referring to the previous question, was replication incorporated?
Yes, because each treatment group had 20 subjects.
Does the study described incorporate the principle of replication?
Yes, because there were 281 students in one group and 311 in the other group (more than one individual per treatment group)
Which of the following is a categorical variable?
Zip Code
What is the probability that a randomly selected man is shorter than 65 inches?
0.0475
What proportion of the "single" respondents have Job Grade 3?
0.15
What is the probability that a randomly selected man is between 72 and 77 inches tall?
0.2415
Why can we say that the probability model shown below is a correct probability model?
All of the above: Because all of the probabilities are between zero and one Because the sum of all the probabilities is equal to one Because there is a probability assigned to each event
Using the Standard Normal Table, what is the z-score with an area of 0.6808 to its left?
0.47
For incoming freshman at BYU, ACT scores are Normally distributed with a mean of 28 and a standard deviation of 2. How many standard deviations away from the mean is an ACT score of 31?
1.5
What is the upper limit of the control chart for this process?
15.6
The following Normal curve models the heights of women aged 20 to 29. What is the mean height of these women?
64.0 inches
What statistical procedure should be used to answer this research question? (finance graduate salary scenario)
A one-sample t-test for means
Suppose we take a random sample of size 60. What is the probability that the mean of the 60 times is less than 479.4 minutes?
0.0020
What type of variable is the explanatory variable?
Categorical
A librarian is interested in how many books an average visitor checks out. She keeps a tally of how many books are checked out by each visitor as she scans them. What type of sample is this?
Convenience sample
True or False: The researchers decided that it was too expensive to sample as many as was required from their calculations. To decrease the required sample size and therefore the cost, they could increase their confidence level and decrease the desired margin of error.
False
When checking the condition of "normality of the population of differences," you check the two separate sample plots for outliers or extreme skewness.
False
Where can you find the writing assignment instructions?
From their Learning Suite assignment pages
What are the conditions for one-sample t-procedures?
Normality of the population or large sample size, and randomness in the data collection
Suppose we are testing H0: μ = 10 versus Ha: μ < 10. The upper right hand curve represents the sampling distribution of x̄ when H0 is true; the lower left hand curve represents the sampling distribution of x̄ when Ha is true. What is the color of the area that represents α if μ is really 10?
Red (area to the left of the line on the top curve)
What is the parameter we are interested in?
The mean difference between the absorption rate of the reference drug and the absorption rate of the generic drug for all potential users
Which of the following statements is false?
The p-value is the probability that the null hypothesis is true.
Is the normality condition met for this test?
Yes, since both histograms have no outliers.
What is the parameter of interest to compare the proportions from two populations?
p1-p2
What is the standard error of p-hat?
0.011
On the left panel, select "Z Procedures for Proportions", then select "One Sample". Select the "Student Responses" dataset, then select the "StickShift" variable to test. Generate a bar chart of the data, then create a table of counts below the bar chart. We want to estimate the proportion of BYU students who know how to drive a stick shift vehicle. Proceed to statistical inference. What is the value of p-hat, or the sample proportion of students who know how to drive a stick shift vehicle?
0.297
Suppose we took samples of size 40 instead of 18. What will be the shape of the sampling distribution of x̄?
Approximately Normal
The following situation applies to the next three questions: R.A. Fisher, a famous statistician, describes a well-known design in his book, Design of Experiments. Five varieties of wheat were compared to determine which gave the highest yield in bushels per acre. Eight farms were available for planting. Each farm was divided into five plots. For each farm, the five varieties were randomly assigned to the five plots with one variety per plot. The varieties were planted on their assigned plots and their yields were measured and compared. 2. What type of study is this?
Experiment - randomized block design
Which one of the following graphs best represents the correct shaded area under the curve for z < -1.8 and z > 0.67?
Graph 4
The department of motor vehicles wants to check whether drivers have a slower reaction time after drinking two cans of beer. This was done by selecting a sample of 19 drivers and randomly assigning them to one of the two groups. The reaction times (measured in seconds) in an obstacle course are measured for a group of 10 drivers who had no beer. The other group of 9 drivers were given two cans of beer each and their reaction times on the same obstacle course are measured. What are the correct null and alternative hypotheses for this test? Use "N" for no beer and "B" for two cans of beer.
H0: μN = μB vs. Ha: μN < μB
On the left panel, select "Z Procedures for Proportions", then select "Two Sample". Select the "Student Responses" dataset, then select "PoliticalParty" to define your populations and "CapitalPunishment" as the variable to test. Select "Democrat" as Group 1 and "Republican" as Group 2. Generate bar charts of your data. Select "Proceed to Statistical Inference". Select "Support the use of the death penalty" as your response variable. We want to test if the proportion of BYU students who identify as Democrat and support the death penalty is less than the proportion of BYU students who identify as Republican and support the death penalty. What is our alternative hypothesis? (Hint: Assume p1 is pDemocrat and p2 is pRepublican).
Ha: p1 < p2
What does the statistical term "population" refer to?
It refers to the group we want to study or learn something about
A researcher wanted to compare the reaction time of students on a Driving Skills Test while using a cell phone and while not using a cell phone. 32 students were tested under both conditions with the order randomized (i.e., a coin was tossed and if heads, reaction time using cell phone was tested first; if tails, reaction time without a cell phone was tested first). The resulting data should be analyzed using the following procedure:
Matched pairs t-test for means
Who are the subjects in this study?
Ninth-grade students enrolled in a general mathematics course
Suppose we take a sample of size n = 20 from this same population. Can we compute the probability that x̄ is less than 100?
No, because we cannot apply the Central Limit Theorem. Thus, the sampling distribution of x-bar is not approximately normal.
Researchers wanted to determine the proportion of all rap artists who wear grills. They surveyed 180 rap artists from Los Angeles and their responses were recorded. They reported their 90% confidence interval to be (0.06, 0.14). Is this a valid confidence interval?
No, it does not state that the sample was random
Suppose we have a left-skewed population distribution with a mean of 30 and a standard deviation of 3. For random samples of size 18, what will be the shape of the sampling distribution of x̄?
Not approximately normal - the Central Limit Theorem does not apply
Assume all the conditions of this test have been met. If the p-value is .010, what can we conclude at α = 0.05?
Reject the null hypothesis and conclude that at least one mean differs from the other means.
Suppose the p-value is 0.0034. What is the correct conclusion to make at α = 0.01?
Reject the null hypothesis and conclude that the mean amount spent on textbooks by undergraduates is less than $300.
Suppose the p-value was 0.034. What conclusion should we make at α=0.05 ?
Reject the null hypothesis and say that we have sufficient evidence to conclude that the true proportion of heart attacks for those who take aspirin is less than those who take a placebo.
What is the major difference between an observational study and an experiment?
Researchers assign treatments to subjects in an experiment.
A computer manufacturer has just received a shipment of 8000 computer chips. In order to ensure that the shipment meets their quality standards, they want to sample a few chips and make a detailed examination of the sample. The chips are packaged individually and have serial numbers. If they use a statistical software package to randomly select serial numbers for 20 chips for inspection, what type of sampling is this?
Simple random sample
The college of humanities in a large university was accused of discrimination in their faculty hiring. Twenty records of the recent female applicants who were not hired and twenty records of recent male applicants who were not hired were randomly selected and compared with the records of the recent hires. What type of sampling design is this?
Stratified sample
To estimate the average time taken to complete the Stat 121 final exam, instructors randomly selected 150 students that had previously taken the course and recorded their time on the test. The instructors then calculated a 98% confidence interval to be (98, 142) minutes. What is the parameter the instructors are trying to estimate?
The mean time taken by all students on the Stat 121 final exam
A machine is known to produce 20% defective products and is therefore sent for repair. After the machine is repaired, the manager of the factory wants to ensure that the machine is functioning properly. 400 products produced by the machine are chosen at random, and 64 of them are found to be defective. What is the appropriate null hypothesis?
The proportion of defective products produced by this machine is equal to 0.20
The following information applies to questions 9-10. Go to https://rconnect.byu.edu/Stat121App/ On the left panel, select "Sampling Distribution of X-bar". Assume the population is right-skewed. Experiment with various sample sizes of your choosing. What happens to the shape of thesampleas the sample size increases?
The sample becomes more and more like the population distribution.
Which of the following is NOT a way we can meet the condition of the normality of the sampling distribution of x̄?
The sample standard deviation is not large
Assume the population is still right-skewed. What happens to the shape of the sampling distribution of x-bar as the sample size increases?
The sampling distribution of x-bar becomes approximately normal.
No late credit quizzes or writing assignments will be accepted.
True
The purpose of statistics is to convert data into useful information.
True
True or False: Statistical inference can be defined as making generalizations about the population based on sample data.
True
True or False: The name of this quantity, sigma over square root of n, is the standard error of x̄.
True
True or False: The symbol for the sample standard deviation is "s".
True
True or False: When comparing the z-distribution and the t-distribution, both have the same center at 0.
True
Without random selection, we cannot appropriately apply the laws of probability to perform inference.
True
A university official wants to determine if a relationship exists between whether college students choose their majors before their junior year and whether they graduate from college. For this study, what is the response variable?
Whether a student graduates from college
A researcher wanted to learn more about the relationship between whether or not a student getting less than 8 hours of sleep the night before a test determines whether or not they pass their test the next day. What is the explanatory variable in this study?
Whether or not a student got less than 8 hours of sleep the night before a test
Consider the following metabolic rates: 1772 1666 1362 1460 1867 1439 1614 Suppose the first number in the data set was 1972 instead of 1772. How would this change the value of the median?
Would not change the median
Calculate the standard deviations of the plant weights in each group. Is the equal population standard deviation met?
Yes, .79/.44 equals 1.80, which is less than 2.
Calculate the standard deviation of the nightly amount of sleep for each group. Is the equal standard deviation condition met?
Yes, 0.99/0.85 is less than 2.
Is this study described above a valid experiment?
Yes, all of the principles for a valid experiment are met.
Was using the eight farms as blocks appropriate?
Yes, because it removes lurking variables from farm to farm.
If the textbook committee makes a histogram of the sample data and it is single-peaked with no outliers, are the conditions of randomness and normality of the population met for this test?
Yes, because it was a random sample and the plot of the sample data has no outliers
Is the sampling distribution of p-hat approximately normal in this example?
Yes, because np > 10 and n(1-p) > 10
Were the data appropriately collected for performing a two-sample z test on proportions?
Yes, because the 22,071 subjects in the study were randomly allocated to either the aspirin group or the placebo group.
Is the normality condition met for this test? Below are boxplots of the data:
Yes, because the boxplots show no outliers
The conditional distributions of job grade for each marital status are given in the following table. On the basis of the these conditional distributions, is there a potential association between marital status and job grade?
Yes, because the conditional distributions differ from each other
A 90% confidence interval was found to be (-0.45, -0.13). Suppose that we were instead testing a two-sided hypothesis. Does this confidence interval allow us to say that the two proportions differ significantly at α = 0.10?
Yes, because the confidence interval does not include 0.
The following scenario applies to questions 9 - 10: Go to Link (Links to an external site.) On the left panel, select "Procedures for Means", then "One Sample T Procedures". Select the "Crabs" dataset, then select the "frontallobesize" variable to test. Generate a histogram of the data. Are the conditions met to conduct a one-sample t test for means on the average size of a crab's frontal lobe?
Yes, because the plot of the sample data has no outliers.
Who should be contacted if you had an emergency and missed a due date, or you have an accommodations letter and need to adjust a deadline, or you are an athlete/performer/etc. and will be traveling during a midterm?
the course coordinator
What is the parameter of interest?
The difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer
In context, what was the control used in this study?
86mg of Placebo
A study was performed in order to find out if having your cellphone out, even if you never check it, affects productivity. 250 BYU students in the finance program volunteered for the study, which lasted the course of one semester. All the students were taking the same classes and the students were randomly assigned to either have their phone out for the first half of the semester or the second half. Fifty students were in the "phone out second half" group and 200 students were in the "phone out for first half" group. The average amount of time it took to finish their homework was recorded. What is the individual in this study?
A student
When can you see the correct answers for each Credit Quiz?
After the due date
A sample of 12th grade students who took the National Assessment of Education Progress year 2000 mathematics test had a mean score of 250. What is the population?
All 12th grade students who took the National Assessment of Educational Progress year 2000 mathematics test
Researchers for the National Institute of Child Health and Human Development studied 208 infants whose brains were temporarily deprived of oxygen as a result of complications at birth. These babies were subjects in an experiment to determine if reducing body temperature for three days after birth improved their chances of surviving without brain damage. What is the population?
All babies who were temporarily deprived of oxygen as a result of complications at birth
What time do midterms close on the last day of the exam?
All exams close at 4:00 PM MT on the last scheduled day of the exam.
Is the right hand generally stronger than the left in right-handed people? You can crudely measure hand strength by placing a bathroom scale on a shelf with the end protruding, then squeezing the scale between the thumb below and the four fingers above it. The reading of the scale shows the force exerted. Which of the following best describes the design of a matched pairs experiment to compare the strength of the right and left hands using 10 right-handed people as subjects?
Each subject squeezes the scale twice: once with his right hand and once with his left hand with the order randomly determined. Scale readings are then compared.
In context, what is the subject in the experiment?
Individual volunteers
What is the final step in the Big Picture of Statistics, as outlined in class?
Inference
The following information will be used for questions 8-10. Go to https://rconnect.byu.edu/Stat121App/. On the left panel, select "Exploratory Data Analysis". Select the "Student Responses" dataset, then select the "MonthsEngaged" variable to explore. Generate a histogram of the MonthsEngaged data, then calculate the 5 Number Summary using the feature below the graph.
Median, because the histogram is skewed to the right.
What type of bias results when people respond differently to questions asked by male interviewers than they do to questions asked by female interviewers?
Response bias due to interviewer effect
In statistics, how do we define the probability of an event?
The relative frequency with which the event occurs in a long series of trials
Choose the following option which best describes the following histogram using shape, center, and spread
This histogram looks right skewed with a center of about 12 and a spread ranging from 0 to 50
The placebo effect happens when subjects improve because they have confidence in the medical provider and hope in the medication, even when they may not be receiving the treatment.
True
When sampling from the population of interest, it is a good idea to have a representative sample.
True
Which of the following best answers whether or not an outlier is present in the following histogram?
Yes, the data value at 48 is very far out and not near any other data points.
n August 27, 1995, an article in the Los Angeles Times reported that in a survey of 3297 California adults, 2780 (83.4%) had health insurance coverage. These results have a margin of error of1.4%. What type of study is being described?
an observational study
Proceed to the statistical inference. Using the sliding bar, calculate a 90% confidence interval to estimate the average weight of an NBA player.
(213.81, 214.49)
The average height of BYU freshman from a random sample of 450 freshman at BYU is 68 inches with a standard deviation of 1.5 inches. What is the 98% confidence interval for the average height of BYU freshman?
(67.83, 68.17)
Choose the probability that best matches the following statement: "This event is impossible; it cannot occur."
0.0
Suppose the t-statistic was -3.25. What is the associated p-value?
0.0005 < p-value < 0.001
Suppose the test statistic was -3.17. What is the associated p-value?
0.0008
Suppose that the test statistic was -3.00. What is the p-value for this test?
0.002 < p-value < 0.005
Calculate a 95% confidence interval. What is the margin of error?
0.16
Ezra's friend, Gwen, takes the math portion of the ACT and scores 27. ACT math scores are Normally distributed with a mean of 20.7 and a standard deviation of 5.0. What is the z-score for Gwen's ACT score?
1.26
The following situation applies to the next four questions: Ezra scores 680 on the mathematics portion of the SAT. The distribution of SAT math scores in recent years has been Normal with a mean of 518 and a standard deviation of 114. What is the z-score for Ezra's SAT math score?
1.42
Assume that all conditions are met. The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. What is the test statistic for this procedure?
1.59
What is the z* associated with 95% confidence?
1.960
Which of the following is most likely the center of the histogram?
10.02
What is the value of Q3?
102.0
Given the table below, what is the conditional distribution of marital status for males in Job Grade 3?
2%, 96.2%, 1.4%, 0.4%
Proceed to statistical inference and conduct a one-sample t test for means to test if the average size of a crab's frontal lobe is greater than 15 mm. What is the test statistic?
2.359
What is the value of σ, the standard deviation of heights?
2.70 inches
Looking at the following boxplot, what number does the third quartile correspond to?
5
How was randomization incorporated into this study?
All five varieties were randomly assigned to the five plots at each farm.
Referring to the confidence interval given in the previous question, what would be the correct decision to make for the test of hypotheses with H0: μY = μS vs. Ha: μY ≠ μS at α = 0.05?
Because 0 is not included in the interval, we reject the null hypothesis and conclude that the means are different.
Consider the following confidence interval interpretation: "We are 98% confident that the true mean laptop screen size is between 19.2 and 21.4 inches". Is this interpretation of a confidence interval correct or incorrect? Why or why not?
Correct. It gives all three parts of confidence interval interpretation.
Which of the following is NOT a part of hypothesis testing?
Creating an interval estimate
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. What is the name of the correct procedure that should be used for this study?
Experiment - matched pairs t test for means
The term "population" can only be applied to people.
False
True or False: If results are statistically significant, then they are also of practical importance.
False
True or False: Important differences are always statistically significant if a small sample size is used.
False
What are the null and alternative hypotheses?
H0: μ = 2 vs. Ha: μ ≠ 2
Suppose the textbook committee of a certain college department is interest in studying the amount of money that their undergraduate students spent on textbooks the previous semester. The chair of the committee believes that the mean amount spent on textbooks is less than $300. A random sample of 120 students was taken and the following statistics were calculated: x̄ = 293 and s = 27. What are the appropriate null and alternative hypotheses for this test?
H0: μ = 300 vs. Ha: μ < 300
In order to assess the evidence provided by the sample data, what is the appropriate question to ask?
How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?
Three of the following are correct statements about probabilities and one statement is incorrect. Which statement is NOT correct?
If two events cannot occur simultaneously, then the probability that either occurs cannot be computed.
Consider the following confidence interval interpretation: "The mean of all laptop screen sizes lies between 12.47 and 15.59". Is this interpretation of a confidence interval correct or incorrect? Why or why not?
Incorrect. It does not give a level of confidence
Can we compute the probability that x̄ is less than 29 for n=18?
No, because the population is not Normally distributed and we cannot apply the Central Limit Theorem
To investigate the effects of the drug phen-fen, 200 women in the 30-40 age range who had used the drug for at least one year were located. 200 women of the same age group who had not used the drug were also located. The incidence of heart valve abnormality was compared between the two groups. What type of study is this?
Observational Study
An experiment that doesn't incorporate randomization is NOT a valid experiment.
True
If the p-value is less than α, then the results are statistically significant.
True
True or False: 14 should be considered an outlier.
True
True or False: Power is the probability of rejecting a false null hypothesis.
True
Suppose our sample size was reduced to 25 instead of 35. Would it still be appropriate to calculate the probability that the sample mean is greater than 12 years?
Yes, because the population is normal, the sampling distribution of x-bar is still normal.
Which one of the following is the correct representation of the margin of error?
z* times sigma over square root of n
Suppose a 95% confidence interval was made to estimate the monthly cost of Internet service instead of a 90% confidence interval. Fill in the blank: The 95% confidence interval will be _______ the 90% confidence interval.
wider than
What is the best estimate for Q1 for visitor times?
5
Suppose that on a farm there are 3 cows, 5 horses, and 10 chickens. If you randomly select one farm animal, what is the probability of selecting a horse?
5/18
The following information will be used for questions 5-6. The stem plot below represents data taken from a study on the amount of time students spend doing homework everyday. Stem-and-Leaf Plot of Time spent on homework (in minutes), n=43 Note: 04|2 equals 42 04|124 05|2456 06|35788 07|344467 08|2456999 09|455889 10|12368 11|0226 12|678 5. What is the value of Q1?
68.0
Why do we sample?
All of the above: A census may be too expensive, A census may be time consuming, A census may be impractical
What does the distribution of a random variable give us?
All possible values of the random variable and how often they occur
For the above distribution, which of the points represents where the median would lie? Points A, B, and C show the three measures of center.
B
Based on the boxplots below, which has the lowest median?
Boxplot 3
What type of relationship is this?
C --> C
What is the role - type classification of the variables in this study?
C-->C
Students at a particular university are able to evaluate professors on a five point scale (a score of 1 meaning poor teaching and a score of 5 meaning excellent teaching, with answers limited to a whole number). What type of random variable is professor evaluation an example of?
Discrete
What is the most appropriate measure of spread for this data, and why?
IQR, because the boxplot is skewed to the right.
What is the alternative hypothesis in this example?
Male and female scholarship athletes do not have the same mean GPA
Why is the randomization condition met for performing this procedure?
Six subjects were randomly selected from the twelve to receive the generic drug first and the remaining six to receive the reference drug first
How do the medians for IQ scores compare for the boxplots above?
The median for male IQ scores is greater than the median for female IQ scores
The mean and median selling price of existing single-family homes sold in October 2005 were (in no particular order) $216,200 and $265,000. Which of the following most accurately explains which is the mean and which is the median and why? (Hint: Although most single-family homes are around this price range, there are a small number of multi-million dollar homes.)
The median is $216,200 and the mean is $265,000 because economic variables tend to be skewed to the right, pulling the mean above the median.
Suppose that the p-value was calculated to be 0.07. How would you interpret the p-value in context?
The probability of obtaining a sample mean of Litetop weights as extreme or more extreme than 2.04lbs assuming the population mean is 2lbs is equal to 0.07.
Which of the following describes statistical power in this situation?
The probability of sending a patient with a medical problem to the doctor.
What is the appropriate alternative hypothesis?
The proportion of defective products produced by this machine is less than 0.20
True or False: Suppose we take all possible samples of the same size from a population and for each sample, we compute x̄. The mean of these x̄ values will be exactly equal to the mean of the population (μ) from which the samples were taken.
True
True or False: The median is the midpoint of the distribution. It is the number such that half of the observations fall above it, and half fall below it.
True
According to the National Health and Nutrition Survey (NHANES) sponsored by the U.S. government, a random sample of 712 males between 20 and 29 years of age and a random sample of 1,001 males over the age of 75 were chosen and the weight of each of the males were recorded (in kg). Do the data provide evidence that the younger male population weighs more (on average) than the older male population? Use "Y" for ages 20-29 and "S" for ages 75+. It was found that x̄Y = 83.4, sY = 18.7, x̄S = 78.5, sS = 19.0. Suppose the confidence interval was (3.546, 6.254). What is the correct interpretation of this confidence interval?
We are 95% confident that the true difference between the mean weight of males 20-29 and the mean weight of males 75+ lies between 3.546 and 6.254 kg.
Consider the control chart below. Is the process out of control?
Yes, there is a run of 9 or more consecutive points on the same side of the center line.
If there is not enough evidence to support the alternative hypothesis, we can accept the null hypothesis.
False
The null hypothesis is the claim that the researcher wants to prove.
False
The p-value gives the probability that the null hypothesis is true.
False
Suppose Ezra's z-score is 1.50 and Gwen's z-score is 1.20. If we assume that both assessments measure the same kind of ability, who did better: Ezra or Gwen?
Ezra
Looking at the side-by-side boxplots from the previous question, should the mean for boxplot #3 be less than, greater than, or roughly equal to its median?
Less than
Refer to the process described in the block description. On the basis of the following sample means, can we say that the process is "in control"?
No, because there is a run of nine or more x̄'s either above the center line or below the center line.
On the basis of this grouped bar chart from a similar study, can we conclude causation? (Can we conclude that changing marital status causes changes in job grade?)
No, because this is an observational study
Two treatments were applied to two groups of children - one group receiving the active treatment, which included them covering a unit on shapes. The other group received the passive treatment, which did not include a unit on shapes. The number of shape identifications made by each child was recorded as the response. What is the response variable?
Number of shapes identified
Which of the following intervals corresponds to the largest area under a Normal curve?
Q1 to (μ + 2σ)
What type of variable is "number of texts sent in response?"
Quantitative
Suppose researchers calculated the 95% confidence interval to be (0.4125, 0.4675). What is the correct interpretation of this interval?
We are 95% confident that the true proportion of all U.S. adults who spend more than 20 hours a week on a computer at home lies between 0.4125 and 0.4675.
How quickly should you expect a response after sending an email to the professors, course coordinator, or TAs?
Within two school days
Calculate a 98% confidence interval to estimate the proportion of students who can drive a stick shift vehicle. What is the margin of error?
0.026
Suppose the t test statistic is t = 1.72. What is the p-value for a two-sided test?
0.10 < p-value < 0.20
Let X be the number of girls the couple has. Based on the eight arrangements, what is the probability that X = 2?
0.375
What proportion of those who were Divorced were in job grade 2?
0.556
The following scenario applies to questions 1-4: A population is known to have a Normal distribution with a mean of 180 and a standard deviation of 36. Suppose that all possible samples of size 20 were taken. What would be the mean of the sampling distribution of x̄ ?
180
What is the IQR?
2
Suppose the researchers wanted to calculate a 90% confidence interval with a margin of error of 0.04. How many rap artists need to be randomly sampled?
423
What will be the standard deviation of the sampling distribution of x̄ if samples of size 20 are taken?
8.05
Approximately what percentage of the heights are less than 66.7 inches?
84%
What statistical procedure should be used to answer this research question? (Canadian air traffic controller scenario)
A one-sample z-confidence interval for proportions
Suppose that this study was a two-sided test using an α = 0.04 with the null and alternative hypotheses being H0: μ = 2 versus Ha: μ ≠ 2. A 96% confidence interval was calculated to be (1.99lbs, 2.05lbs). What should the conclusion be?
Fail to reject H0 since 2 is inside the given interval.
Suppose that the p-value was 0.0259. What is the appropriate conclusion to make if α = 0.05?
Reject H0. We have sufficient evidence to conclude that the mean concentration is different from 250 ppm.
All college students in the U.S. have a mean age of μ = 21.3 in 2014. Suppose you randomly select two samples of students from this population, and you calculate the sample mean for each. Sample 1 has a size of n = 200, and Sample 2 has a size of n = 40. Which sample is more likely to get a sample mean of 24 or more?
Sample 2 is more likely
Select "Proceed to Statistical Inference". We want to test if more than 6% of BYU students are from Texas. Select the "Yes" category to test. Using the appropriate hypotheses, enter the correct claimed proportion and symbol for Ha to calculate the test statistic and p-value. Assuming that α = 0.05, what is the appropriate conclusion we should make?
Since our p-value is less than 0.05, we reject the null hypothesis and conclude that more than 6% of BYU students are from Texas.
In order to estimate the mean age to be diagnosed with diabetes, a researcher takes a sample and finds the mean age to be 16.4. What is the parameter of interest?
The mean age of all people at which they were diagnosed with diabetes
What is the purpose of a statistical control chart?
To distinguish between natural and unnatural variation.
Is the randomness condition met for this test?
Yes, because a random sample was taken.
Use the slider bar to calculate a 95% confidence interval at the bottom of the computer output. If we wanted to use a confidence interval instead of a hypothesis test to see if there is a significant difference in sleep between married and non-married BYU students, would we make the same conclusion as your previous answer?
Yes. Because the confidence interval contains only positive values, that would imply that married students get more sleep than non-married students.
How can you earn extra credit in Stat 121?
All of the above
Suppose that p̂ is 0.6 and the standard error of p̂ is 0.025 and that all conditions are met. Compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.
(0.551, 0.649)
The weights of all of the Utah County Fair pigs have an unknown mean and known standard deviation of σ = 18. A simple random sample of 100 pigs is found to have a sample mean weight of x̄ = 195. Calculate a 95% confidence interval for the mean weight of all Utah County Fair pigs.
(191, 199)
What is the test statistic for this study?
-2.00
Calculate the test statistic for this test.
-2.5
What is the test statistic for this test?
-2.84
What is the probability that a random sample of 35 adults will have a mean greater than 12 years of education?
0.0055
Using the Standard Normal Table, what is the area to the left of z < -2.34?
0.0096
Suppose the conditions were all met and the test statistic is t = 2.560. What is the associated p-value?
0.01 < p-value < 0.02
Suppose the actual test statistic is z = -2.30. What is the associated p-value?
0.0107
In the 1980's, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? The purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks. What proportion of those who received the placebo had a heart attack?
0.017
The following situation applies to the next two questions: The distribution for the number of courses students take at a particular university is listed as follows: Number of Courses 1 2 3 4 5 6 7 Probability 0.02 0.03 0.09 0.25 0.40 0.16 0.05 What is the probability that students take only one or two courses?
0.05
What is the value of p-hat, or the sample proportion of students who are from the state of Texas?
0.072
What proportion of visitor times are at least 40 minutes?
0.10
The average American male has a BMI of 28.6 and having a BMI over 25 is considered obese. In a random sample of 200 men across the US, the sample mean x̄ was found to be a BMI of 26.8. It is known that the population standard deviation σ = 1.7. What is the standard deviation of the sampling distribution of x̄?
0.12
The following situation applies to the next two questions: A couple plans to have three children. There are eight possible arrangements of girls and boys. For example, GGB means that the first two children are girls and the third child is a boy. All eight arrangements are (approximately) equally likely. Write down all eight arrangements of the sexes of three children. Based on the eight arrangements, what is the probability of obtaining any one of these arrangements?
0.125
Suppose we have a right skewed population distribution where μ = 109 and σ = 32. For random samples of size n = 100, what is the probability of getting an x̄ greater than 112?
0.1736
Quiz 24A - Now select "Normal Probability Calculator" on the left panel. Use this application to compute the probability that more than 14% of a random sample of 95 Broadway shows run for 1-2 years. First use the drop-down menu to select the correct shaded area for the probability. To calculate the Z-score, use the sample proportion you calculated in the previous question as the value for p, the proportion of all Broadway shows that run for 1-2 years.
0.2743
The following information applies to questions 8-10. Go to https://rconnect.byu.edu/Stat121App/ On the left panel, select "Normal Probability Calculator". Suppose the average adult has completed an average of 11.25 years of education with a standard deviation of 1.75 years. Assume this distribution is normal. 8. What is the probability that a randomly selected adult has completed more than 12 years of education?
0.3336
Suppose we take a sample of size n = 50 from this same population, and we calculate x̄ = 540 minutes. How many standard deviations, (σ/ √n), away from μ is this sample mean?
0.53
What is the probability that students take at least five courses (i.e., five courses or more)?
0.61
Using the Standard Normal Table, what proportion of observations on the Standard Normal Curve lie between z = -1.8 and z = 0.67?
0.7127
What is the probability that any random sample of n = 100 results in an x̄ between 106.5 and 115.9?
0.7669
The following information applies to questions 8-10. Open https://rconnect.byu.edu/Stat121App/ On the left panel, select "Normal Probability Calculator". Assume that heights of adult men are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected man is taller than 67 inches?
0.8413
We sometimes hear that marriage is good for your career. An SRS of 8235 male managers and professionals employed by a large manufacturing firm were asked their marital status (married, single, widowed, or divorced) and their job title. (To avoid gender effects, the investigators looked only at men.) The researchers categorized their jobs into one of four job grades (1, 2, 3, or 4). Grade 1 contains the jobs in the lowest quarter of the job grades, and Grade 4 contains those in the highest quarter. Their results are contained in the following table. What proportion of Job Grade 1 who were surveyed said that they are Married?
0.92
What are the appropriate degrees of freedom for this test?
119
What is the lower limit of the control chart for this process?
14.4
In order to construct an x̄-chart for this process, what number should be used as the center line?
15.0
If the researcher wanted to have 90% confidence in the results with a margin of error of 6.8, how many pigs must be sampled?
19
Regardless of confidence level, what will the center of our confidence interval be?
214.15
Approximately what percentage of the heights are between 61.3 and 64 inches?
34%
Proceed to statistical inference. The CDC says that adults need at least 7 hours of sleep per night. Conduct a hypothesis test to see if the average amount of sleep BYU students get is different than 7 hours per night. Assuming that α = 0.05, what is the appropriate conclusion to make?
Because the p-value is greater than 0.05, we fail to reject Ho and have insufficient evidence to conclude that the average amount of sleep that BYU students get is significantly different than 7 hours a day.
Normal curve G has a mean of 50 and a standard deviation of 5. Normal curve H has a mean of 50 and a standard deviation of 10. How do the shapes of these two Normal curves compare if they are drawn using the same scale?
Both are centered at 50, but curve G is taller and skinnier than curve H
The Law of Large Numbers states that as the number of trials increases, the relative frequency of an event gets further and further from the theoretical probability.
False
Suppose the z-score for Gwen's Math ACT score is 1.2, what is the correct interpretation of this z-score?
Gwen's ACT score is 1.2 standard deviations above the mean
A certain prescription medicine is supposed to contain an average of 250 parts per million (ppm) of a certain chemical. If the concentration is higher than this, the drug may cause harmful side effects; if it is lower, the drug may be ineffective. The manufacturer runs a check to see if the mean concentration in a large shipment conforms to the target level of 250 ppm or not. A simple random sample of 100 portions is tested, and the sample mean concentration is found to be 247 ppm. The sample concentration standard deviation is s = 12 ppm. What are the appropriate null and alternative hypotheses?
H0: μ = 250 vs. Ha: μ ≠ 250
In order to determine if there is a difference between the mean GPA of male and female scholarship athletes, a university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that the mean GPA (grade point average) of a random sample of 40 male scholarship athletes is 3.02 and the mean GPA of a random sample of 36 female scholarship athletes is 3.11. If there is no difference in the mean GPA of male and female athletes, the probability of obtaining this difference (3.11 - 3.02 = 0.09) or more extreme is approximately 0.287. What is the null hypothesis in this example?
Male and female scholarship athletes have the same mean GPA
There are various sources of flickering lights in our environment; for instance, light from computer screens and fluorescent bulbs. Whether or not the human eye can detect the flicker depends on its frequency. A 1973 study ("The effect of iris color on critical flicker frequency," Journal of General Psychology [1973], 91- 95) obtained data from a random sample of 19 subjects and recorded eye color and Critical Flicker Frequency (CFF), a numerical measure of threshold sensitivity to flickering light. Do the data suggest that threshold sensitivity to flickering light is related to eye color? What are the correct null and alternative hypotheses? (In this problem, μBI = mean threshold sensitivity for blue eyes, μG = mean threshold sensitivity for green eyes, and μBr = mean threshold sensitivity for brown eyes)
H0: μBl = μG = μBr vs. Ha: at least one mean is different
What are the appropriate hypotheses for this test?
H0: μd = 0 vs. Ha: μd ≠ 0
Suppose the p-value is 0.0336. What is the correct interpretation of this p-value in context?
If the proportion of defective products produced by this machine is equal to 0.20, the probability of getting a statistic as extreme or more extreme as that observed is 0.0336.
Consider the following confidence interval interpretation: "We are 95% confident that we have found a confidence interval that contains the true mean number of Utah high school students involved in a car accident per month". Is this interpretation of a confidence interval correct or incorrect? Why or why not?
Incorrect. It does not state the actual confidence interval
A study of child preferences for milk chocolate was performed. Based on sample results, researchers were 95% confident that the proportion of children that liked milk chocolate was between .75 and .93. What type of inference is being used?
Interval estimation
A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 8% are worn out at 60,000 miles. A study was done and researchers were 98% confident that the proportion of tires that are worn out at 60,000 miles lies between 7.8% and 9.6%. What type of statistical inference is this?
Interval estimation
The 2015 American Time Use Survey contains data on how many minutes of sleep per night an average college student gets. According to this survey, the minutes that college students sleep per night are right skewed with a mean of 529.9 minutes and standard deviation 135.6 minutes. Suppose we take a random sample of size 20. What is the probability that the mean of the 20 times is greater than 538 minutes?
It is not appropriate to calculate probabilities in this situation.
Quiz 24A - What is the shape of the data distribution?
It is not appropriate to determine shape for categorical data.
Four of the following statements are correct descriptions of a Normal curve. Which one is NOT a characteristic of a Normal curve?
Its spread increases as its mean increases
On the left panel, select "ANOVA". Select the "Plant Growth" dataset, then select "group" as your categorical explanatory variable and "weight" as your quantitative response variable. Generate boxplots of your data. According to the boxplots, is the normality of the populations condition met?
No, at least one of the boxplots has at least one outlier.
The following sample means were collected by taking random samples of size n = 25. These sample means were computed from samples taken from a Normal population with μ = 52.4 and σ = 7.5. On the basis of these sample means, can we conclude that the process is "in control"?
No, because at least one of the means is either below the lower control limit or above the upper control limit.
Suppose a study was being done in which 3 sample means were being compared. Below are confidence intervals of the data from this study. Based on these confidence intervals, would you believe that the samples have been taken from three groups that have the same population means? Why or Why not?
No, because one or more of the confidence intervals do not overlap with any of the others
A university professor does not believe that there is no difference between the GPA of male and female scholarship athletes, so he looks into how the sample was collected. His investigation shows that the study was given to all of the scholarship athletes on the basketball teams exclusively. Based on this information, should the university administration trust the results from this study?
No, because the study was not taken from a random sample of scholarship athletes
In order to estimate the mean age to be diagnosed with diabetes, a researcher takes a sample and finds the mean age to be 16.4. What type of statistical inference is this?
Point estimation
Suppose the actual p-value is 0.0336. On the basis of this p-value, what should you conclude at 𝛼 = 0.05?
Reject H0. The proportion of defective products produced by this machine is less than 0.20.
Your company markets a computerized medical diagnostic program used to evaluate thousands of people. The program scans the results of routine medical tests (pulse rate, blood tests, etc.) and refers the case to a doctor if there is evidence of a medical problem. The program makes a decision about each person. The hypotheses are: H0: The patient is healthy. Ha: The patient has a medical problem. Which of the following describes a Type I error in this situation?
Sending a healthy patient to the doctor.
Assume all conditions are met. Select "Proceed to Statistical Inference." Calculate the test statistic and p-value. Assuming that α = 0.01, what is the appropriate conclusion to make?
Since the p-value is greater than 0.01, we fail to reject the null hypothesis and have insufficient evidence to conclude that at least one plant group's mean weight is different.
Select "Proceed to Statistical Inference". Assuming the conditions are met, we want to test whether the amount of sleep is different between married and non-married BYU students. Calculate the test statistic and the p-value. Assuming that α = 0.05, what is the appropriate conclusion we should make? Note: Remember that p-values are probabilities, so they will be decimal values between 0 and 1. A number like "6.732e-02" is written in scientific notation, where the numbers after "e" tell you how many places to move the decimal to the left, so 6.732e-02 in scientific notation would be written as 0.06732 in standard notation.
Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in hours slept between married and non-married BYU students.
Calculate the test statistic and p-value. Assuming that α = 0.05, what is the appropriate conclusion we should make?
Since the p-value is less than 0.05, we reject the null hypothesis and have sufficient evidence to conclude that BYU students who identify as Democrat favor capital punishment less than students who identify as Republican.
What happens to the margin of error as you increase the confidence level?
The margin of error increases.
Suppose the researchers decided to take a sample of size 200 rather than that of 81. How would this change the margin of error?
The margin of error would decrease
In order to estimate the mean age to be diagnosed with diabetes, a researcher takes a sample and finds the mean age to be 16.4. What statistic is used to estimate the parameter of interest?
The mean age of diagnoses for the sample
An administrator in a very large company wants to estimate the mean level of nitrogen oxides (NOX) emitted in the exhaust of a particular car model in their very large fleet of cars. Historically, nitrogen oxide levels have been known to be Normally distributed with a standard deviation of 0.15 g/ml. What statistic is used to estimate the parameter of interest?
The mean level of nitrogen oxide of a sample of cars of a particular model in the very large fleet
An administrator in a very large company wants to estimate the mean level of nitrogen oxides (NOX) emitted in the exhaust of a particular car model in their very large fleet of cars. Historically, nitrogen oxide levels have been known to be Normally distributed with a standard deviation of 0.15 g/ml. What is the parameter of interest that the administrator wants to estimate?
The mean level of nitrogen oxide of all cars of a particular model in the very large fleet.
A laptop company ThinClick claims to have the lightest laptop out on the market, the Litetop, with a reported weight of 2.0 lbs. A laptop review company wasn't sure about this claim and thinks it is different, so they took a sample of 260 Litetop laptops and calculated a mean weight of 2.04 lbs. What is the parameter of interest?
The mean weight of all Litetops
A manufacturing process produces bags of cookies. The weights of these bags are known to be normally distributed and should have a mean of μ = 15.0 ounces with a standard deviation of σ = 0.4 ounces. In order to monitor the process, four bags are selected periodically and their average weight (x̄) is computed. What is the parameter of interest?
The mean weight of all bags of cookies produced by this manufacturing process.
If all possible samples of size 80 are taken instead of size 20, how would this change the mean and standard deviation of the sampling distribution of x̄?
The mean would stay the same and the standard deviation would decrease
Two studies were done on the same set of data, where study A was a two-sided test and study B was a one-sided test. The p-value of the test corresponding to study A was found to be 0.040. What is the p-value for study B?
The p-value must be 0.020
True or False: A z-score measures how many standard deviations an individual value is from the mean.
True
True or False: ANOVA falls under a C → Q role-type classification.
True
Is the equal population standard deviation condition met for this test? Below are the sample standard deviations for each group: Blue StDev: 1.53 Green StDev: 1.37 Brown StDev: 1.84
Yes, because (largest standard deviation) / (smallest standard deviation) is less than 2.
Refer to the process described in the block description. On the basis of the following sample means, can we say that the process is "in control"?
Yes, because all of the means vary between the lower and upper control limits.
Is the normality of the sampling distribution condition for performing a two-sample z test on proportions met?
Yes, because all of the np checks are greater than 5
A process is being monitored using an x̄-chart. Sample means were computed from random samples of size n = 16 from a Normal population with μ = 35.0 and σ = 5.0. On the basis of the following x̄-chart, can we say that the process is in control?
Yes, because all the x̄'s are between the upper and lower control limits and there are only four in a row above the center line.
A study was conducted in order to estimate the proportion of U.S. adults that use a computer at home more than 20 hours a week. Suppose 36 out of a random sample of 81 adults use a computer at home more than 20 hours a week. Is the sample size large enough to compute a confidence interval for the proportion of U.S. adults who spend more than 20 hours a week on a home computer?
Yes, because both np̂ and n(1-p̂) are greater than 10
The following information applies to the next three questions. Go to https://rconnect.byu.edu/Stat121App/ On the left panel, select "Procedures for Means", then "One Sample T Procedures". Select the "Student Responses" dataset, then select the "Caffeine" variable to test. Generate a histogram of the data. Is it appropriate to calculate a one-sample t confidence interval for means to estimate the average number of caffeinated drinks consumed by BYU students?
Yes, because our sample size is bigger than 30.
The following information applies to questions 9-10. Go to Link. On the left panel, select "Procedures for Means", then "One Sample T Procedures". Select the "Student Responses" dataset, then select the "HoursSleep" variable to test. Generate a histogram of the data. Are the conditions met to perform one-sample t procedures for means on the average amount of sleep by BYU students?
Yes, because our sample size is large enough.
Does this study incorporate the principle of control/comparison?
Yes, because the group of students receiving only traditional instruction can be considered a control group. The group of students receiving the additional instruction of probability-statistics can be considered the active treatment comparison group.
The following information applies to questions 8-10. Go to https://rconnect.byu.edu/Stat121App/ . On the left panel, select "Procedures for Means", then "One Sample T Procedures". Select the "NBA Players" dataset, then select the "Weight" variable to test. Generate a histogram of the data. Is it appropriate to calculate a one-sample t confidence interval for means to estimate the average weight of an NBA player?
Yes, because the sample histogram appears to be normal.
Fill in the blanks: The sample proportion, ____, is used to estimate the population proportion, ____.
p hat, p
Suppose a sample of 200 was taken instead of 100. How will the margin of error change?
the margin of error will decrease in size
Suppose a sample of 200 was taken instead of 100. How will the margin of error change?
the margin of error will increase in size
Choose the probability that best matches the following statement: "This event is very unlikely, but will occur once in a while in a long sequence of trials."
0.05
Choose the probability that best matches the following statement: "This event is less likely to occur, but it is not extremely unlikely."
0.3
The following table gives the results from 1000 females and their heights. Height (inches)5862677175 Probability0.20.40.20.10.1 What is the probability that a female is 62 inches or less in height?
0.6
Choose the probability that best matches the following statement: "This event is extremely likely, but occasionally it will not occur in a long sequence of trials."
0.90
The following information applies to questions 8-10. Go to R Shiny App https://rconnect.byu.edu/Stat121App/ and on the left panel, select "Exploratory Data Analysis". Select the "NBA Players from 1976 - 2016" dataset, then select the "AST." (assists) variable to explore. Generate a histogram of the Assists data. What is the approximate overall spread of the data? Hint: Under "Numerical Exploratory Data Analysis," select the "5 Number Summary" as the summary to calculate. As part of the output, it will give you the maximum and minimum data values (labeled "Max" and "Min"), which will help you answer this question.
100
Calculate the five number summary of the following data set. 2127302228 2028192822
19, 21, 24.5, 28, 30
Late Exams (after the exam has closed) will be subject to which of the following penalties?
20% score reduction for the first day, 10% penalty for each additional day
Approximately how many NBA players averaged less than 5 assists a game?
3000
The following data, as summarized in the stem plot below, were collected in a study about the number of pirates in the world.Stem-and-Leaf Plot of Pirates, n=35Leaf Unit = 1.01|01 2|2259 3|3444 4|67999 5|0335779 6|34577 7|8889 8|4569|2 What would be the value of the median?
53
Does this study described incorporate the principle of randomization?
Yes, because we are told that "students ... were randomly allocated ..."
Which of the following is not part of the Big Picture of Statistics?
Publishing data
In the 2010 census, the US government asked residents the following question: "How many people were living or staying in this house, apartment, or mobile home on April 1, 2010?" What type of variable would the answer be?
Quantitative
When a patient goes to the emergency room or urgent care, the medical staff needs to know how much pain the patient is in. They often ask something like "with no pain being a 0, difficult but able to work through the pain being a 5, and the worst pain you've ever felt being a 10, how much pain are you in?" to gauge the patient's pain level. What type of variable would the answer be?
Quantitative
Consider the following two survey questions: Question 1: How satisfied are you with your current job: very satisfied, somewhat satisfied, somewhat dissatisfied, very dissatisfied? Question 2: What do you think can be improved about your job? Which of the following statements is true?
Question 1 is a closed question and Question 2 is an open question
The following scenario applies to the next four questions: Scientists want to investigate the effects of caffeine on short term memory by randomly assigning 200 volunteers to intake 86mg of caffeine before a memory quiz and the remaining 200 volunteers to intake 86mg of a placebo before taking a memory quiz. The quiz score of each volunteer is recorded. What is the response variable?
Quiz score
The following information applies to questions 8-10. Go to https://rconnect.byu.edu/Stat121App/. On the left panel, select "Exploratory Data Analysis". Select the "Student Responses" dataset, then select the "HoursInternet" variable to explore. Generate a boxplot of the HoursInternet data, then calculate the 5 Number Summary using the feature below the graph. 8. Using the boxplot and 5 Number Summary, what is the value above which an individual's daily time on the Internet is considered to be an outlier?
6
The following situation applies to the next two questions: A shoe manufacturer wanted to determine which type of material, "Material X" or "Material Y", to use on the soles of their shoes to get maximum wear. Twenty teenage boys wore one shoe with each type of sole. For each young man, a coin was tossed; if heads, "Material X" would go on the right shoe and "Material Y" on the left. If tails, "Material X" would go on the left shoe and "Material Y" on the right. After wearing these shoes for four months, the thickness of the sole of each shoe was measured. 5. What type of study is this?
A matched pairs experiment.
A study of computer-assisted learning examined the learning of "Blissymbols" by children. Blissymbols are pictographs (think of Egyptian hieroglyphs) that are sometimes used to help learning-impaired children communicate. The researcher designed two computer lessons that taught the same content using the same examples. One lesson required the children to interact with the material, while in the other the children controlled only the pace of the lesson. Call these two styles "Active" and "Passive", respectively. Children were assigned at random to Active and Passive groups. After the lesson, the computer presented a quiz that asked the children to identify 56 Blissymbols. What type of study is this?
Experiment
The following situation applies to the following seven questions: Because more questions about statistics have been added to the state exam, a school district decided to add a probability-statistics unit to their ninth-grade general mathematics course. To determine whether the unit will have an impact on scores on the state exam, all ninth-grade students enrolled in a general mathematics course in the largest high school in the new school district were randomly allocated into two groups. One group of 281 students received instruction in a new probability and statistics unit in addition to the traditional instruction; the other group of 311 students received only traditional instruction. Students in both groups were given the state exam at the end of ninth grade to determine whether the group receiving additional instruction in probability and statistics had a higher average score than the group receiving just traditional instruction. 1. Is this study an observational study or an experiment?
Experiment
An experiment must have a placebo group in order to be valid.
False
Convenience sampling is a type of probability sampling design.
False
In studies of worker productivity, it has been noticed that any change in the work environment together with the knowledge that a study is underway will produce a short-term increase in productivity. This is known as
Hawthorne effect
A large university in the western United States wants to survey the faculty regarding its plan to combine the spring and summer terms into one semester. It randomly selects 5 colleges on its campus and from each of these colleges, randomly selects 4 departments. Within the chosen departments, 4 faculty members are selected to be included in the sample. What type of sampling design is this?
Multistage sample
Suppose you have played a game many, many times — winning sometimes and losing sometimes. Can you use the results of playing the game to predict with absolute certainty whether you will win the game on the next try?
No
Because of concerns about employee obesity and related health problems, a very large company conducted a study to compare two weight-reducing programs (low-carb diet and low-fat diet). Forty employees volunteered to participate in the study for a 10-week period. Half of the employees were randomly assigned to the low-carb diet and the other half randomly assigned to the low-fat diet. What type of study is this?
Randomized Controlled Experiment
Which of the following is a false statement about statistics?
Statistical information is never misleading or misrepresented.
Which one of the following statements is true regarding credit quiz and assignment scores?
The four lowest scores will be dropped from grade calculations except Credit Quiz 01 and both writing assignments
When are credit quizzes due on Learning Suite?
They are due before midnight (11:59 PM MT) according to the quiz schedule on Learning Suite.
A sample is a subgroup of the population.
True
What is the shape of the following stem and leaf plot
Uniform