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