Stats Final Exam Review
Event
A collection of outcomes
Margin of Error
A measure of precision of the confidence interval estimate.
Probability
A measure of the likelihood of an event happening
Confidence Intervals
A range of numbers believed to include an unknown population parameter generated by a point estimate
Intersection
AND
Sample Space
All possible outcomes
Central Limit Theory
As N increases, the population of all sample means become normally distributed, no matter what the sample population distribution.
Normal Distribution
Bell shaped curve
Pulled Variance
Can use if both sample variances are within 3X of each other
P value
Comparing two probabilities with each other
Critical Value
Comparing two z values
Discrete random variables
Countable variables
The empirical rule tells us that, for bell shaped curves, approximately a. 68% of the data lie within one standard deviation of the mean b. 95% of the data lie within two standard deviations of the mean c. 99.7% of the data lie within three standard deviations of the mean D all of the above
D all of the above
The method of determine probability which is base don the self-beliefs of persons involved in the experiment is classified as the ________ approach a subjective b objective c frequency d classical
a subjective
Continuous random variable
Data can have infinite values
T Test is used for
Dependent, independent means
Complimentary
Everything else
Chi-Square Test
Examines two categorical distributions Tests whether the distributions percentages are different enough to say that they differ statistically.
After ANOVA breaks down the total variability in the response (Y) variable into two parts (differences between the treatment means and differences within the treatments), a ratio is formed which serves as the test statistic for testing the null hypothesis that all of the underlying treatment populations means are equal. Which distribution does this ratio follow? t-distribution Normal distribution Chi-square distribution F-distribution z-distribution
F-distribution
Events that are independent cannot be mutually exclusive True or False
False
True or False: In an ANOVA application, the alternative hypothesis states that all of the treatment means are equal.
False
When performing a chi-square test of independence, the sample size is large enough to assume the test statistic has an approximate chi-square distribution as long as which two of the following states are valid? No more than 1/5th or 20 % of the expected values should be less than 5 Every expected value is at least 5 Every expected value is greater than 0 Every Expected value is at least 1 The data is normally distributed
No more than 1/5th or 20 % of the expected values should be less than 5 Every Expected value is at least 1
Z Distribution
Normally Distributed
Union
OR
If HA has a greater or less than symbol
One-tailed test
Mutually Exclusive
Outcomes have nothing in common
Uniform Distribution
Probabilities are the same of all values of x
Poisson Distribution
Probability of a given number of events occurring in fixed interval of time.
P value method
Probability of attaining the sample results if the sample results are true.
Level of Significance
Represents the probability of a type 1 error
Histograms
Shape of distribution
Dependent samples
Subjects selected in first do affect the second
Frequency is
Summarizes categorical data
Alternative Hypothesis
The claim being made about the parameter
Critical Region
The range of values of z data for which we reject the null hypothesis
Independent samples
The subjects selected for first subjects don't interfere with second selected
Variance
The variance (σ2), is defined as the sum of the squared distances of each term in the distribution from the mean (μ), divided by the number of terms in the distribution (N).
True or False: In ANOVA, a very large F-ratio provides strong evidence that the null hypothesis of equal treatment means is probably false.
True
True or False: In an ANOVA application, the null hypothesis states that all of the treatment means are equal.
True
True/false: The chi-square test for independence is designed to analyze data from a single random sample, which has been cross-classified into the r rows and c columns of a contingency table in order to determine if the row and column variables of the table are statistically independent.
True
True or False: Under certain conditions and assumptions, the analysis of variance (ANOVA) procedure can be used to determine if the mean nighttime viewing distance associated with four different headlight designs are all equal.
True!
Binomial Distribution
Two possible outcomes
If HA has equal to symbol
Two tailed test
Null Hypothesis
What is assumed about the value of the parameter
Which of the following keywords is most associated with a joint probability statement? a AND b Or c NOT D Given
a AND
A combination is a unique subset of size n drawn from a set of size N where the order of the chosen items ____________ matter and repletion of items is _________ a does not, prohibited b does not, allowed c does, prohibited d does, allowed
a does not, prohibited
If we are testing the null hytphesis that the mean is less than or equal to 100 and the critical values for the test is determiend to be z = 1.645, then the rejection region would be all of the z values that are _____________ 1.645 a greater than b less than c greater than or equal to d less than -1.645 or greater than +1.645
a greater than
The ___________ distribution is a discrete probability distribution that provides probabilities for the number of occurrences of some event over a given period, interval, distance, or space; it is typically used to model the occurrences of rare events. a poisson b binomial c complementary d supplementary
a poisson
The test statistic (zData) looks at the difference between what we actually see in the real world and what we expect to see in the real world. A _________ test statistic is a strong indication that the null hypothesis should probably ____________, whereas a _____________ test statistic tells us that we should probably ____________ the null hypothesis, as it is likely to be false. a small; not to be rejected, large reject b small, be rejected, large, not reject c. large, not to be rejected, small reject d large not to be rejected, small, modify
a small; not to be rejected, large reject
If the random variable x is normally distributed, _______ percent of all possible observed values of x will be within three standard deviations of the mean. a. 68.26 b. 95.44 c 99.73 d 100 e None of the above
a. 68.26
Which of the following is NOT a common measure of variability? a. Median b. Variance c Standard Deviation d. Range
a. Median
Critical values are used to designate the critical region (________) for a hytphesis test. a. rejection region b confidence region c probability region d disorder region
a. rejection region
The _____ is he set of all possible ____ for an experiment. For example, consider the experiment of rolling a twenty sided die. The _____ for rolling the die could be resented as S= 1-20 a. sample space, outcomes, sample space b sample event, outcomes, sample event c. sample event, sample spaces, sample event outcome, sample spaces, outcome
a. sample space, outcomes, sample space
If we looked at a very large number of intervals with a 95% confidence level, approximately ___________ of them would fail to include the actual population mean a 95% b 5% c most d all
b 5%
The ___________ of an event is a number that measures the likelihood that an event will occur when an experiment is carried out a Outcome b Probability c Intersection d Observation
b Probability
Whether or not a randomly selected university student is majoring in business is an example of... a. a quantitative variable b a qualitative variable c could be either a qualitative or qualitative variable d neither a qualitative or qualitative variable
b a qualitative variable
The mean is usually our first choice for describing the central tendency of a data set; however it can be affected by extreme values. In such cases, its best to choose a measure of central tendency that is more resilient to the pull of extreme values; the __________ is quite often a suitable option. a average b median c mode d range
b median
For any particular sample size, the standard error for the mean is euqal to the ________________ a population standard deviation multiped by the square root of the sample size b population standard deviation divided by the square root of the sample size c. population mean multiplied by the square root of the sample size d. population mean divided by the square root of the sample size
b population standard deviation divided by the square root of the sample size
Stats is typically divided into which of the following categories? a. Descriptive and deductive statistics b. descriptive and inferential statistics c. Deductive and inferential stats d. Both A and B
b. descriptive and inferential statistics
Unlike the ________ hypothesis, the _______ hypothesis is not assumed to be true at the outset of the hypothesis test. It is only supported if the same evidence is significant. a alternative, null b. null, alternative c. alternative, zero d. alternative, alternative
b. null, alternative
A table provides data on 8 before and after statistical averages. The appropriate hypothesis test for this scenario is the... a. one tample test of mean b. two-sample test of mean, dependent samples c. two-sample test of mean, independent samples d. two-sample test of proportion
b. two-sample test of mean, dependent samples
The area under the standard normal curve between z = 1 and z = 2 is ________________ the area under the normal curve between z =2and z = 3 .a.Less than b.Greater than c.Equal to d.A, B, or C above, depending on the value of the mean e.A, B, or C above, depending on the value of the standard deviat
b.Greater than
A joint probability is equivalent to a(n) __________ probability multiplied by a(n) __________ probability .a.sample;population b.conditional; marginal c.independent; mutually exclusive d.descriptive; inferential
b.conditional; marginal
The type of probability distribution whose standard deviation is oneand mean is equal to zero is classified as a __________ distribution. a.weighted probabilities b.standard normal probability c.normal cumulative probability d.approximated normal
b.standard normal probability
A manufacturerer tested a sample of capacitors and found that 20 were defective and 290 were good. If additional tests are to be conducted with random samples of 185, find the mean for the expected number of defects in these groups of 185 a 8 b 10 c 12 d. 20
c 12
How many different ways coulda committee of five members be selected from a group of 20 professors? a 100 b 108 c 15,504 d 1,860,480
c 15,504
The type of data collection in which every measurement of interest is selected is called a what? a Population b Sample c Census d Parameter
c Census
The area under the standard normal curve between z=1 and z=2 is _____________ the area under the normal curve between z= -2 and z=-1 a. less than b Greater than c Equal to D A, B, or c, depending on the mean E A b or C, depending on the standard deviation
c Equal to
Events which can never occur together are classified as ___________ events a collectively exclusive events b mutually exhaustive events c mutually exclusive events d collectively exhaustive events
c mutually exclusive events
The collection of all of the possible outcomes of a random experiment is called its a numerical space b domain space c sample space d both b and c
c sample space
If occurrence of a statistical event A does not affect occurrence of event B and vice versa then these events are classified as a.statistically dependent events b.descriptive unaffected events c.statistically independent events d.statistically unaffected even
c.statistically independent events
ANOVA test always
checks for equality of means across samples, our hypotheses will always take the form: μ1=μ2=μ3......μk.
Which of the following represents a continuous random variable: 1 The number of clicks an online ad gets 2 The number of books Amazon sold from noon to 3pm 3 The number of people on a flight from LA to Australia 4 The time fast food customers are waiting for their orders a 1,3,4 b 1,2,3 c. 2 and 3 d 4 only
d 4 only
Which of the following is/are an example(s) of a hypothesis in the context of statistics? 1. The unemployment rate is more than 5% 2. An airline claims that its on time arrival is greater than 95% 3. A mayor touts that wind turbines provuide greater than 20% of the power to a local community 4. A manaager of a popular restaruant claims that her restaurant table turnaround time has decreased by 10 minutes a 1,3,4 b 1,2,4 c 2,3 d All four
d All four
Curves (Z or t) with greater variation (__________) will be flatter on top and more spread out. a correlation b variance explained c a lower standard deviation d a higher standard deviation
d a higher standard deviation
A conditional probability is equivalent to a ______ probability divided by a ________ probability a sample and population b independent, mutually exclusive c marginal, joint d joint, marginal
d joint, marginal
A discrete random variable is a variable that can a not be an integer b be any positive or negative number c assume any continuous value d only assume a countable number of values
d only assume a countable number of values
For a left tailed hypothesis test, the p value is the area under the normalcurve____________ a that includes the test statistic b to the right of the test statistic c that includes all possible values of z d to the left of the test statistic
d to the left of the test statistic
Suppose that a quiz consist of 20 True and False Questions. A student hasn't studied for the exam and will just randomly guess at all the answers. How would you find the probability that the student will get 8 or fewer answers correct? a. Find the probability that x = 8 in a binomial distribution with n = 20 and p =0.5 b. find the area between o and 8 in a uniform distribution that goes from 0 to 20 c. find the probability that x is less than or equal to 8 for a normal distrubiton with the mean of 10 and standard deviation of 5 d.find the probability that x is less than or equal to 8 in a binomial disputation with n=20 and p=0.5
d.find the probability that x is less than or equal to 8 in a binomial disputation with n=20 and p=0.5
The binomial distribution is a continuous distribution true or false
false
True or false: When performing a chi-square test of independence, we can assume the test statistic has an approximate chi-square distribution as long as every expected value is at least one.
false
True/false: The null hypothesis in a chi-square test of independence always hypothesis that the variables are statistically dependent.
false
Z test is used for
independent proportions
Degrees of freedom
number of values in the final calculation of a statistic
Frequency distribution
numerical data
Consider a variable that follows a normal distribution. If the value of μ is 75 and the standard deviation of the distribution is unknown, a value of x = 120 implies that the value of the z-statistic will be a.one b.zero c.negatived .positive .unknown
positive
T distribution
standard deviation not known S used as a substitute Flatter
True or False: The Chi-Square Goodness of Fit Test is designed to determine if a set of frequencies (counts) follows a particular probability distribution.
true