STAT 2023 Final
What value of p should be used in the formula of estimating sample size for population proportions if we don't have any prior information? 0.25 0.5 0 1
0.5
In an experiment of tossing a die, what is the sample space? odd numbers even numbers 1, 2, 3, 4,5, 6 none of the above
1,2,3,4,5,6
There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.
False
In a binomial experiment, the results of one trial are dependent on the results of other trials.
False One assumption of the binomial distribution is independence of trials.
The sampling distribution of x¯x¯ must be a normal distribution with mean = 0 and standard deviation = 1.
False Sampling distribution does not have to be a normal distribution.
Which one below is quantitative? Gender Hair Color Height Letter Grade
Height
A data set that records the hair color of a sample is a qualitative data. True False
True
Which of the following is a point estimate of the slope of the simple linear regression? epsilon x b1 b0
b1
All of the following are assumptions of the error terms in the simple linear regression model except errors are normally distributed. error terms have a mean of zero. error terms have a constant variance. error terms are dependent on each other.
error terms are dependent on each other.
If the mean, median, and mode for a given population are all equal and the relative frequency curve has matching tails to the right and left, then we would describe the shape of the distribution of the population as ________. bimodal skewed to the right symmetrical skewed to the left
symmetrical
When testing the difference between two population proportions using large independent random samples, the ________ test statistic is used. z t F chi-square None of the other choices is correct.
z
What does the uniform distribution look like? Too complicated to describe An "S" shaped curve A unimodal curve A horizontal line
A horizontal line
In forming a confidence interval for μ1 − μ2, only two assumptions are required: independent samples and sample sizes of at least 30.
False
The range of the measurement is the largest measurement plus the smallest measurement.
False
When comparing two independent population means, if n1 = 13 and n2 = 10, degrees of freedom for the t statistic is 22.
False Degrees of freedom = n1 + n2 − 2 = 13 + 10 − 2 = 21
For any sampled population, the population of all sample means is approximately normally distributed.
False Only for populations that are a normal distribution. According to the CLT, if the sample sizes are 30 or greater, the sample means are approximately normally distributed.
An example of a quantitative variable is the manufacturer of a car.
False. This is an example of a qualitative or categorical variable
An example of a qualitative variable is the mileage of a car.
False. This is an example of a quantitative variable.
In an experiment of flipping a coin, what is the sample space? None of the above Head and Tail Tail Head
Head and Tail
Which one can be used to graphically describe quantitative data? Bar chart None of the above Histogram Pic chart
Histogram
Which in the following is (are) used to describe the central tendency of a data set? Check all that apply. Mean Range Median Mode
Mean Median Mode
A ________ displays the frequency of each class with qualitative data and a ________ displays the frequency of each class with quantitative data. histogram, stem-and-leaf display bar chart, histogram scatter plot, bar chart stem-and-leaf, pie chart
bar chart, histogram The histogram and stem-and-leaf are used to graphically display quantitative data; a scatter plot is used for displaying the relationship between two variables.
If events A and B are mutually exclusive, then P(A|B) is always equal to zero.
True This means that either one or the other has to occur - they both cannot occur at the same time.
A Type I error is rejecting a true null hypothesis.
True This means that you thought there was enough statistical evidence to reject the null hypothesis in favor of the alternative, but there is not.
If p = .8 and n = 50, then we can conclude that the sampling distribution of pˆp^ is approximately a normal distribution.
True. the sample size is larger than 30
What is the correct rejection region for the left tailed z test? Z* > Zα Z* < Zα Z* > -Zα Z* < - Zα
Z* < -Za
Sample mean is ________ the population mean. greater than less than a point estimator of equal to
a point estimator of
When constructing a confidence interval for a population mean, if a population is normally distributed and a small sample is taken, then the distribution of X¯ is based on the ________ . z distribution t distribution neither the z nor the t distribution both the z and the t distribution
t distribution.
A financial analyst working for a financial consulting company wishes to find evidence that the average price-to-earnings ratio in the consumer industry is higher than the average price-to-earnings ratio in the banking industry. The alternative hypothesis is μconsumer = μbanking. μconsumer ≤ μbanking. μconsumer > μbanking. μconsumer < μbanking. μconsumer ≠ μbanking.
μconsumer > μbanking.
Which of the following divides quantitative measurements into classes and graphs the frequency, relative frequency, or percentage frequency for each class? histogram dot plot stem-and-leaf display scatter plot
histogram. A box plot does not easily group measurements into classes; a scatter plot is for looking at the relationship between two variables.
In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels, the cholesterol levels of 9 heart patients are measured before they are given the drug. The same 9 patients use XZR for two continuous months. After two months of continuous use, the cholesterol levels are measured again. The comparison of cholesterol levels before versus after administering the drug is an example of testing the difference between two means from independent populations. two population variances from independent populations. two population proportions. matched pairs from two dependent populations.
matched pairs from two dependent populations. Since it is the same 9 patients, the measurements are not independent. They are related and thus you need to use matched pairs.
Which formula of the degrees of freedom is correct? Assume n is for the sample size. n-1 2n n+1 n
n-1
In the simple linear regression, what is the degrees of freedom of SSE? Let's denote n for the sample size. n n-2 n-1 n+1
n-2
What is the number of degrees of freedom for the test of significance of the slope and y-intercept in a simple linear regression model? n+1 n-1 n n-2
n-2
The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is np ≥ 5. n(1 − p) ≥ 5. np ≤ 5. n(1 − p) ≤ 5 and np ≤ 5. np ≥ 5 and n(1 − p) ≥ 5.
np ≥ 5 and n(1 − p) ≥ 5.
Which of the following hypothesis looks like a null hypothesis? p ≠ 0.5 p = 0.5 p > 0.5 p < 0.5
p = 0.5
Which percentile describes the first quartile, Q1? 25th 50th 75th 100th
25th. This is denoted at Q1; a value below which approximately 25 percent of the measurements lie.
How large the sample size should be for the application of the central limit theorem? 50 40 20 30
30
According to this video, how many properties a binomial random variable has? 2 3 4 5
4
What are the assumptions for the error term in the simple linear regression? Check all that apply. Independence Zero mean Normality Constant variance
All
What shape of a binomial distribution may look like? Symmetrical Skewed to the left All of the above is possible Skewed to the right
All of the above is possible
What question(s) you may ask yourself if you want to determine whether a given random variable is a discrete random variable? Check all that apply. Is it finite? Is it discrete? Is it a random variable? Is it binary?
Is it discrete? , Is it a random variable?
If a population distribution is known to be normal, then it follows that the sample mean must equal the population mean. the sample mean must equal the population mean for large samples. the sample standard deviation must equal the population standard deviation. the sample mean must equal the population mean, the sample mean must equal the population mean for large samples, and the sample standard deviation must equal the population standard deviation. None of these answers is correct.
None of these answers is correct. If the population distribution is known to be normal than you do not need to have a particular sample size; everything else will still be an estimate of the population parameter.
A new company is in the process of evaluating its customer service. The company offers two types of sales: (1) Internet sales and (2) store sales. The marketing research manager believes that the Internet sales are more than 10 percent higher than store sales. The null hypothesis would be PInternet − Pstore > .10. PInternet − Pstore < .10. PInternet − Pstore ≥ .10. PInternet − Pstore ≤ .10. PInternet − Pstore = .10.
PInternet − Pstore ≤ .10. Since you are trying to prove that internet sales are greater than the store sales, the null would be the opposite where the difference between the internet and store sales would be less than .10 or equal to .10.
In the sample size determination, if the calculated sample size (n) is not an integer, what you should do? round it down to the nearest integer None of the above leave as it is. round it up to the nearest integer
Round it up to the nearest integer
When a population is large and we can only afford to measure a sample of elements, which type of statistics has to be used in order to make inference about the population from the sample? Statistical Inference None of them. Descriptive Statistics Both of the above two.
Statistical Inference
What are the properties of normal distribution? Check all that apply. Symmetrical Bell shaped Skewed to the right Skewed to the left
Symmetrical, Bell shaped
In which of the following are the two events A and B always independent? A and B are mutually exclusive. The probability of event A is not influenced by the probability of event B. The intersection of A and B is zero. P(A|B) = P(B|A). The probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A).
The probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A). All of the other options describe dependent events.
A continuous probability distribution that has a rectangular shape, where the probability is evenly distributed over an interval of numbers, is called a uniform probability distribution.
True
A sample is a subset of the population. True False
True
A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.
True
After you have successfully translated your question from the plain language to statistical notations, for example, P(Y=2), what is the immediate question you may want to ask yourself to guide you towards the next step? What is the median of Y? What is the mean of Y? What is the variance of Y? What is the distribution of Y?
What is the distribution of Y?
When testing a hypothesis about a single mean, if the sample size is 51 and the population standard deviation is known, the correct test statistic to use is ________. r z t p-value
z
Which of the following variable(s) is (are) quantitative? Select all that apply. Letter grade of a course Body Weight Gender Time
Body Weight, Time
The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)? 0 1 1/6 1/14
0 For a continuous random variable, probability at a single value = 0.
A manager has just received the expense checks for six of her employees. She randomly distributes the checks to the six employees. What is the probability that exactly five of them will receive the correct checks (checks with the correct names)? 1 1/2 1/6 0 1/3
0 If five have received the correct check, then it follows that the sixth employee will receive the correct check. Thus, the probability that exactly five will receive the correct check is 0.
If the random variable, X, is normally distributed and has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ)/σ are μ and σ. XX and s. 1 and 0. 0 and 1.
0 and 1.
Which of the following are part of the five-number summary? check all that apply. Mean Variance 25th percentile Median
25th percentile, median
Which percentile describes the third quartile, Q3? 25th 50th 75th 100th
75th
If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 10, n2 = 10, the degrees of freedom for the t statistic is ________. 19 18 9 8 10
9 Degrees of freedom = n − 1 = 10 − 1 = 9 for the paired difference test.
When the population is small and all elements can be measured, which type of statistics is more appropriate? Both of above two. Descriptive Statistics None of them. Statistical Inference
Descriptive Statistics
To test if the two independent population have equal variances, we use ___________. No test is needed F test t test Z test
F test
A data set that stores individuals' height is a qualitative data. True False
False
In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degrees of freedom for the t statistic is 10.
False
The number of defective pencils in a total lot of 1000 is an example of a continuous random variable.
False A continuous random variable may assume any numerical value in one or more intervals on the real number line. This random variable is discrete.
Mutually exclusive events have a nonempty intersection.
False Mutually exclusive events do not intersect (have no sample spaces in common).
The median is the measure of central tendency that divides a population or sample into four equal parts.
False The median divides a population into two equal parts.
The t distribution always has n degrees of freedom.
False. Degrees of freedom are n − 1.
The population mean is the point estimate of the sample mean.
False. The sample mean is the point estimate of the population mean.
For a fixed sample size, the lower we set α, the higher is the ________. Type I error Type II error random error p-value
Type ll Error
In a simple linear regression analysis, the correlation coefficient (r) and the slope (b) ________ have the same sign. rev: 01_20_2021_QC_CS-247723 always sometimes never
always It shows if there is a positive or negative association o relationship.
Two mutually exclusive events having positive probabilities are ________ dependent. always sometimes never
always Mutually exclusive events are always dependent on each other because if one option occurs the other cannot occur.
When determining the sample size, if the value found is not an integer initially, you should ________ choose the next highest integer value. always sometimes never
always. you should always round up so you can ensure your sample size is large enough.
The ________ measures the strength of the linear relationship between the dependent variable and the independent variable. correlation coefficient distance value Y-intercept residual
correlation coefficient
As the Type II error, β, of a statistical test increases, the power of the test ________. increases decreases stays the same randomly fluctuates
decreases
A stem-and-leaf display is best used to ________. provide a point estimate of the variability of the data set provide a point estimate of the central tendency of the data set display the shape of the distribution display a two-variable treemap.
display the shape of the distribution. It is more difficult to find central tendency and variability using a stem-and-leaf display. It is easy to visualize the shape of the distribution using stem-and-leaf.
A discrete probability distribution is expressed as a table, graph, or ________ that gives the probability associated with each possible value that the random variable can assume. binomial formula Poisson hypergeometric
formula This distribution, no matter how it is displayed, will sum to 1.
What is the rule of thumb that we say sample size is large enough for a Z test of a population proportion? np ≥ 5 np ≥ 5 and n(1-p) ≥ 5 np ≥ 5 or n(1-p) ≥ 5 n(1-p) ≥ 5
np ≥ 5 and n(1-p) ≥ 5
All of the following are used to describe quantitative data except the ________. histogram stem-and-leaf chart dot plot pie chart
pie chart. Pie charts are used only for categorical or qualitative data.
When events A and B are independent, which of the following statement(s) is(are) true? Select all that apply. P(A|B) = P(B) P(A|B) = P(A) P(A) = P(B) P(B|A) = P(B)
P(AlB)=P(A) , P(BlA)= P(B)
An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.
True
Both dot plots and stem-and-leaf displays can be used to detect possible outliers. True False
True
Cumulative frequency distribution is non-decreasing. True False
True
F-distribution has two parameters: numerator degrees of freedom and denominator degrees of freedom. True False
True
Frequency polygon is graphed based on histograms. True False
True
If p = .8 and n = 50, then we can conclude that the sampling distribution of p_hat is approximately a normal distribution. True False
True
If the sampled population is exactly normally distributed, then the sampling distribution of the sample mean is also expected to be normal, regardless of the sample size. True False
True
The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and is such that the probability of success on any trial is the same.
True
The dependent variable is the variable that is being described or predicted.
True
The mean and median are the same for a normal distribution.
True
The mode is the measurement in a sample or population that occurs most frequently.
True
The number of emails you receive on Mondays is a discrete random variable. True False
True
The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
True
Which sample size below makes t-distribution look like the standard normal distribution the most? 40 4 25 19
40
The mean of the binomial random variable is np(1 − p).
False The mean of the binomial random variable is np.
If the sampled population has a mean of 48 and standard deviation of 16, then respectively the mean and the standard deviation for the sampling distribution of x¯x¯ for n = 16 are 4 and 1. 12 and 4. 48 and 4. 48 and 1. 48 and 16.
48 and 4. Mean = 48; Standard deviation = 16/√n = 16/4 = 4
According to this lecture video, how many fundamental elements of hypothesis testing? 3 4 6 5
5
Using the following probability distribution table of the random variable x, what is the probability of x = 3? XP(X)05/1514/1521/153 3/15 5/15 1/15 2/15
5/15 All values of P(X) need to sum to 1, so 5/15 + 4/15 + 1/15 = 10/15 means P(X = 3) = 5/15.
What is the probability of a random selected sample has a value within 2 standard deviation around the mean if the population is normally distributed? 95% 99.7% 68% 50%
95%
How large the sample size is large enough for the distribution of the sampling proportion to be approximated normal? At least 5 successes and 5 failures At least 5 failures At least 30 in total At least 5 successes
At least 5 successes and 5 failures
Which of the following statement about the t-distribution is true? Check all that apply. Bell shaped has a smaller variance than the standard normal distribution has a larger variance than the standard normal distribution Symmetrical
Bell Shaped, has a larger variance than the standard normal distribution, symmetrical
Frequency polygon is graphed based on bar chart. True False
False
Two events are independent if the probability of one event is influenced by whether or not the other event occurs.
False
When data are symmetric, median is more common used to describe its central tendency. True False
False
In a statistical study, the random variable X = 1 if the house is colonial, and X = 0 if the house is not colonial. The random variable X is continuous.
False A continuous random variable may assume any numerical value in one or more intervals on the real number line. This random variable, X, is discrete.
Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.
False If the level of significance (α) is less than the p-value, we fail to reject the null hypothesis.
The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.
False The error term is the difference between the observed and predicted values of the dependent variable.
The larger the p-value, the more we doubt the null hypothesis.
False The larger the p-value, the greater the doubt the alternative hypothesis.
If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.
False This example is a description of a hypergeometric distribution.
As the sample size increases, the standard deviation of the sampling distribution increases.
False. Increasing a sample size will cause the standard deviation of the sampling distribution to decrease (because we are dividing the population standard deviation by n).
Daily high temperature in a local community collected over a 30-day time period is an example of cross-sectional data.
False. Cross-sectional data are collected at the same point in time. This is an example of time series data.
Which of the following is the correct way to calculate P( -1.6 < Z < 0.5)? P(Z < -1.6) - P(Z < 0.5) P(Z < 0.5) - P(Z < -1.6) P(Z < -0.5) - P(Z < -1.6) P(Z > 0.5) - P(Z > -1.6)
P(Z < 0.5) - P(Z < -1.6)
During the random sampling, if we put the sampled element back to the population before the next sampling, It is called Sample with replacement Sample without replacement equal sampling unequal sampling
Sample with replacement
________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed. Cluster sampling Sampling error Sampling distribution of the mean The Central Limit Theorem
The central limit theorem.
Variance measures the variation in the data set, namely, how far away the data points deviate away from the center. True False
True
The actual weight of hamburger patties is an example of a continuous random variable.
True A continuous random variable can consist of any numerical value in one or more intervals on the real number line. In this case a hamburger patty could take on any weight
The variable Home Ownership can take on one of two values: 1 if the person living in the home owns the home and 0 if the person living in the home does not own the home. This is an example of a discrete random variable.
True Because this variable has a finite number of possible values (either 0 or 1) it is a discrete random variable.
The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.
True If the sample size is large, then the sampling distribution of the sample mean is approximately normal, even if the sampled population is not normally distributed.
An event is a collection of sample space outcomes.
True It is also called experimental outcomes and only one of these sample space outcomes will occur on a single repetition of the experiment.
If the sampled population is exactly normally distributed, then the sampling distribution of x¯x¯ is also expected to be normal, regardless of the sample size.
True Since the sampled population is normally distributed, then the sample size plays no role.
For a continuous distribution, P(X ≤ 100) = P(X < 100).
True The curve of a random variable x if the probability that x will be in a specified interval of numbers is the area under the curve f(x) corresponding to that interval.
In a symmetric population, the median equals the mode.
True The population is a perfect bell curve.
If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of pˆp^ with a normal distribution.
True The sampling distribution of the sample mean is the probability distribution of the population of all possible sample means that could be obtained from all possible samples of the same size.
When the margin of error is added to and subtracted from the sample mean, an interval is formed that will contain μ with a probability of (1 − α).
True This is the confidence interval with the mean.
The population variance is the average of the squared deviations of the individual population measurements from the population mean.
True This population variance is represented by sigma squared.
A uniform distribution f(x) is a continuous probability distribution, which says the probability that x is in any two intervals of equal length is the same.
True This type of distribution is especially useful for waiting times when they have been arranged into a histogram.
A bar chart is a graphic that can be used to depict qualitative data.
True. A bar chart is a graphic that depicts a frequency, relative frequency, or percent frequency distribution.
Stem-and-leaf displays and dot plots are useful for detecting outliers.
True. Since this graph places the measurements in order from smallest to largest, it allows the analyst to see all of the measurements in the data set.
A discrete random variable may assume a countable sequence or list.
True. It may assume a finite number of possible values or a countable sequence i.e. 1, 2, 3, 4, etc.
The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level for this test is .10, the null hypothesis would be rejected.
True. Since the calculated p-value is less than the significance level you would reject the null hypothesis.
The probability of an event is the sum of the probabilities of the sample space outcomes that correspond to the event.
True. This helps us deal with the uncertainty of an event to determine the likelihood that an event will occur.
The population mean is the average of the population measurements.
True. This mean is calculated by adding all of the population measurements and dividing the resulting sum by the number of population measurements.
A Type II error is failing to reject a false null hypothesis.
True. This means you had enough statistical evidence to reject the null hypothesis in favor of the alternative, but you did not.
Assuming the same level of significance α, as the sample size increases, the value of tα/2 approaches the value of zα/2.
True. With a small sample size, the curve is low and long, and with a larger sample size it approaches the standard normal curve.
A population is a set that includes all elements about which we wish to draw a conclusion.
True. A data set provides information about some group of individual elements, which may be people, object, events, or other entities.
A random sample is selected so that every element in the population has the same chance of being included in the sample.
True. A data set provides information about some group of individual elements, which may be people, object, events, or other entities.
Cross-sectional data are data collected at the same or approximately the same point in time.
True. Cross-sectional data are collected at the same point in time an example would be a specific month for a cell phone bill for several employees or sales during a specific time period.
Statistical inference is the science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.
True. Statistical inference is the process of using randomly selected data to make generalizations or deductions about the population that the random sample was drawn from originally.
In any probability situation, either an event or its complement must occur.
True. The probability of the experiment is that only one of the outcomes will occur.
The number of sick days per month taken by employees for the last 10 years at Apex Co. is an example of time series data.
True. This data is collected over different time periods; specifically 10 different years at Apex Co.
The relative frequency is the frequency of a class divided by the total number of measurements.
True. This is used when we wish to summarize the proportion (or fraction) of items in each class.
A stem-and-leaf display is a graphical portrayal of a data set that shows the data set's overall pattern of variation.
True. This kind of graph places the measurements in order from smallest to largest.
Select all factors that involved in sample size determination. width of the confidence interval confidence level standard deviation Sample mean
Width of the confidence interval, confidence level, standard deviation
What is the correct rejection region for a right tailed z-test of a population proportion when sample size is large? Z* > Zα Z* > - Zα Z* < Zα Z* < - Zα
Z* > Zα
In testing for the equality of means from two independent populations, if the hypothesis of equal population means is rejected at α = .01, it will ________ be rejected at α = .05. always sometimes never
always
What was the trick that I shared with you in the step of calculating the test statistics F*? always assign subscription 1 to the sample with larger sample variance always assign subscription 1 to the sample with smaller sample variance randomly assign subscription 1 to one of the two samples No trick was shared in the video
always assign subscription 1 to the sample with larger sample variance
A random variable is the result of a measurement. can only be discrete. assigns one and only one numeric value to each experimental outcome. is a binomial, Poisson, or hypergeometric variable.
assigns one and only one numeric value to each experimental outcome.
Bar Chart and Pie Chart are used for display __________data? symmetric quantitative non-symmetric qualitative
qualitative
Which of the following graphs is for qualitative data? histogram bar chart ogive plot stem-and-leaf
bar chart. Histogram, stem-and-leaf, and frequency (ogive) graphs display quantitative data.
What are the factors that may affect the width of a confidence interval for the population mean? Check all that apply. confidence level standard deviation sample mean sample size
confidence level, standard deviation, sample size
As standard deviation increases, sample size ________ to achieve a specified level of confidence. increases decreases remains the same
increases
As the sample size ________, the variation of the sampling distribution of x¯x¯ ________. decreases, decreases increases, remains the same decreases, remains the same increases, decreases None of these answers is correct.
increases, decreases
Statistical ________ refers to using a sample of measurements and making generalizations about the important aspects of a population. sampling process analysis inference
inference. By definition, inference is taking a sample of data and its measurements and relating those measurements to the population as a whole.
The cumulative normal table of standard normal distribution provides the probability corresponding to the area under the standard normal curve to the _______ of a z value. left in the middle all the range right
left
The Central Limit Theorem states that as the sample size increases, the distribution of the sample ________ approaches the normal distribution. medians means standard deviations variances
means
If a population distribution is skewed to the right, then, given a random sample from that population, one would expect that the ________. median would be greater than the mean mode would be equal to the mean median would be less than the mean median would be equal to the mean
median would be less than the mean The median in this case would be a better representation of the population - showing where most of the numbers congregate.
The r2 of model 1 and 2 is 0.91 and 0.74, respectively, which model has a better fit? hard to tell model 1 model 2 these two models fit equally well
model 1
What is the degrees of freedom for the t-test of two independent population means when we assume equal variances? Let n1 be the sample size of the first population and n2 be the sample size of the second population. n1 + n2 - 1 n1 + n2 - 2 n1 - n2 n1 + n2
n1 + n2 - 2
The width of a confidence interval will be narrower for 99 percent confidence than for 95 percent confidence. wider for a sample size of 100 than for a sample size of 50. narrower for 90 percent confidence than for 95 percent confidence. wider when the sample standard deviation (s) is small than when s is large.
narrower for 90 percent confidence than for 95 percent confidence. You have a 10% chance of being wrong with a 90% confidence interval and a 5% chance of being wrong with a 95% confidence interval.
When the sample size and the sample proportion p¯ remain the same, a 90 percent confidence interval for a population proportion p will be ________ the 99 percent confidence interval for p. wider than narrower than equal to
narrower than. You are giving yourself 10% chance of error versus only 1% chance of error.
When the sample size is large, what distribution can we assume for the sample proportion? binomial distribution t-distribution normal distribution any distribution
normal distribution
The exact spread of the t distribution depends on the ________. standard deviation of the sample sample size n number of degrees of freedom z distribution
number of degrees of freedom With a large degree of freedoms, the spread will be closer to the normal distribution spread.
A(n) ________ is a graph of a cumulative distribution. histogram scatter plot ogive pie chart
ogive. An ogive is a graph of the cumulative frequency of the class or the cumulative relative frequencies or the cumulative percent frequencies.
Assuming that the null hypothesis is true, the ________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data. α β p-value Type I error
p-value
What is the p-value for a two tailed t test of a population mean? p-value = 2P(t > t*) p-value = 2P(Z > |Z*|) p-value = 2P(t > |t*|) p-value = 2P(Z > Z*)
p-value = 2P(t > |t*|)
What criteria of p-value that FAIL to reject the null hypothesis? p-value < α p-value > α p-value < 0.05 p-value = α
p-value > a
Which of the following statement of p-value is correct? p-value is the smallest probability of making a correct rejection. p-value is the larest probability of making a false rejection. p-value is the smallest probability of making a false rejection. p-value is the largest probability of making a correct rejection.
p-value is the smallest probability of making a false rejection.
Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality, population A will require a larger sample size. population B will require a larger sample size. populations A and B will require the same sample size. None of these answers is correct.
population A will require a larger sample size. This is because of the central limit theorem. Although the sample population is not normal and highly skewed, if there is a large enough sample size, it will start to approach a degree of normality.
If we perform an hypothesis test for the mean, this mean should be: none of above both population and sample mean population mean sample mean
population mean
A ________ is a measure of the chance that an uncertain event will occur. random experiment sample space probability complement population
probability With probability, we are dealing with uncertainty and are applying mathematical models to predict the chance of something occurring.
In the scatter plot of y vs x, if you see y decreases with the increase of x, what you can tell about the correlation coefficient (r)? r = -1 r = 1 r > 0 r < 0
r < 0
All of the following are measures of central tendency except the ________. range mode mean median
range. The range gives the lowest to the highest value in the sample or population.
Which of the following is the right concept of the type I error? reject the null hypothesis when the null hypothesis is true fail to reject the null hypothesis when the null hypothesis is false fail to reject the null hypothesis when the null hypothesis is true reject the null hypothesis when the null hypothesis is false
reject the null hypothesis when the null hypothesis is true
Test statistic is calculated based on_____________(select all that apply). sampled data α, the significant level alternative hypothesis null hypothesis
sampled data, null hypothesis
When we are choosing a random sample and we do not place chosen units back into the population, we are sampling with replacement. sampling without replacement. using a systematic sample. using a voluntary response sample.
sampling without replacement. Sampling with replacement occurs when a selected element is replaced before another sample is taken; systematic and voluntary response samples are not random.
The F distribution is _________________. skewed to the right skewed to the left All of the above could be possible symmetrical
skewed to the right
The least squares regression line minimizes the sum of the differences between actual and predicted Y values. absolute deviations between actual and predicted Y values. absolute deviations between actual and predicted X values. squared differences between actual and predicted Y values. squared differences between actual and predicted X values.
squared differences between actual and predicted Y values.
In this video, what is suggested to start from when given a problem? start from translating the question in the problem from the plain language into statistical notations None of the above start from drawing pictures start solving the problem
start from translating the question in the problem from the plain language into statistical notation
When testing a hypothesis about a single mean, if the sample size is 20, the population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is ________. r z t p-value
t
In testing the difference between the means of two normally distributed populations using independent random samples with equal variances, the correct test statistic to use is the z statistic. t statistic. F statistic. chi-square statistic. None of the other choices is correct.
t statistic.
We use _____ test for a population mean when the population standard deviation is unknown and sample size is small. None of the above F test Z test t test
t test
What test can be used for testing the significance of the slope in a simple linear regression model? t test None of the above F test z test
t test
Which of the following is not a discrete random variable? the number of times a light changes red in a 10-minute cycle the number of minutes required to run 1 mile the number of defects in a sample selected from a population of 100 products the number of criminals found in a five-mile radius of a neighborhood
the number of minutes required to run 1 mile
A simple linear regression model is to study the relationship between ________________. two continuous random variables a continuous and a discrete random variables two discrete random variables any random variables
two continuous random variables
The confidence interval will become _________ if we increase the confidence level from 90% to 95%. narrower not predictable unchanged wider
wider
The t distribution approaches the ________ distribution as the sample size ________. binomial, increases binomial, decreases z, decreases z, increases
z, increases The graph of the t distribution will be short and long with a small sample size and slowly approach the normal curve as the sample size increases.
A standard normal distribution has a mean of ________ and standard deviation of ________. zero, zero zero, one one, one one, zero
zero, one
