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stat101 > skills test 2 > Flashcards

skills test 2 Flashcards

1
Q

what is a factorial

A

a number with a ! after it says you multiply down the numbers as you pick objects

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2
Q

what is the permutations rule

A

select x different objects from n - use where order is important, use PERMUT in excel

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3
Q

what is the combinations rule

A

select x different objects from n - use where order is not important, use COMBIN in excel

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4
Q

what is a random variable

A

takes a single numerical value for each of the random outcomes of an experiment

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5
Q

what is the difference between discrete and continuous random variables

A

discrete - takes isolated values

continuous - takes all values over a range

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6
Q

the mean of a discrete random variable when added up is?

A

1

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7
Q

what is a bernoulli trial

A

a random trial with two outcomes: success or failure

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8
Q

when do you use a binomial random variable

A

when there is a fixed number ‘n’ of identical, independent bernoulli trials where the probability of success for each trial is the same, p.

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9
Q

how do you find expected value with a binomial random variable

A

np

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10
Q

how do you find variance with a binomial random variable

A

npq

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11
Q

what do you do in excel for a binomial random variable

A

BINOM.DIST (number of successes, trials, probability of success, cumulative true or false)

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12
Q

where would cumulative be used in excel

A

where you want excel to count down

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13
Q

where is a poisson random variable used

A

to find the number of independent events that occur randomly over a unit of time or space

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14
Q

how do you find expected value for poisson

A

lambda = mean = expected value

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15
Q

how do you find variance for poisson

A

lambda

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16
Q

what do you do in excel for poisson

A

POISSON.DIST (X, mean/lambda, cumulative true or false)

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17
Q

when using poisson for a binomial problem, what do we equate

A

lambda = np

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18
Q

for a continuous random variable, pr(X=x) = ?

A

0

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19
Q

how do you find the area for a uniform distribution

A

take the distance between c and d (the points you are interested in) and divide that by the total length of the box

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20
Q

what do you do in excel for a normal distribution

A

NORM.DIST (X, mean, standard deviation, cumulative always true)

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21
Q

what is the standard normal distribution

A

where you use z scores to standardise the normal distribution so that the mean is 0 and the standard deviation is 1

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22
Q

when do we use inverse normal

A

when we are given a probability (area) and need to work out the associated x value

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23
Q

how do you do inverse normal questions in excel

A

NORM.INV (probability, mean, standard deviation)

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24
Q

what little formula do we use to rescale random variables

A

Y = aX + b

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25
Q

what is the condition for the dual variance formulas

A

X and Y are independent

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26
Q

the sum or difference of independent normal random variables also has?

A

a normal distribution

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27
Q

what is a point estimation

A

a single value used to estimate a population parameter

28
Q

what is the sampling distribution of a sample statistic

A

this is the distribution of all values of the statistic when all possible samples of the same size n are taken from the population - we think of this as a random variable

29
Q

describe the central limit theorem

A

for a population that is not normally distributed the distribution of the sample means will, as the sample size increases, approach a normal distribution

30
Q

what does the central limit theorem work for

A

populations which were already normal to start with, or non-normal population distributions with large enough samples (greater than or equal to 30)

31
Q

for larger samples we will get a smaller standard error so we expect?

A

less variation between the means of different samples

32
Q

what characteristics are there for proportions

A

success and failure

33
Q

what is p hat (sample proportion)

A

number of successes in sample/sample size

34
Q

when is the sampling distribution of the sample proportion approximately normally distributed?

A

if the sample size n is large enough that we can expect at least 5 successes and at least 5 failures in the sample

35
Q

describe a point interval

A

gives us a confidence interval range of values used to estimate the true value of a population parameter - margin of error with an upper and lower limit

36
Q

how should you interpret an observed confidence interval

A

if the population is repeatedly sampled (with the same sample size) and for each sample the interval is calculated, then ___% of the intervals will contain the true value of the population mean

37
Q

what information do you need to work out a t critical value

A

confidence level (alpha, or 1-confidence interval as a decimal) and degrees of freedom (n - 1)

38
Q

what factors influence the margin of error

A

data variability (standard error), sample size n, confidence interval 100 (1-alpha)%

39
Q

how do you work out the sample error

A

s/square root of n

40
Q

what is the estimate standard error for a population proportion

A

square root of p hat (1 - phat)/n

41
Q

what excel function do you use for a t critical value

A

T.INV.2T

42
Q

what excel function do you use for a z critical value

A

NORM.S.INV

43
Q

what is hypothesis testing

A

this involves starting with some claim or research question about a population and then collecting data to see if this data is in line with the claim

44
Q

what is the notation for the null hypothesis

A

H0

45
Q

what is the notation for the alternative hypothesis

A

Ha

46
Q

the null hypothesis uses what sign

A

=

47
Q

the alternative hypothesis uses what sign

A

greater than, less than or not equal to

48
Q

what is the null hypothesis

A

the statement which is initially assumed to be true

49
Q

how do we standardise to hypothesis test

A

find the test statistic - the number of standard errors away from the null hypothesis value the sample statistic is

50
Q

what is the significance level

A

alpha, the area in the tail(s), probability that has to be chosen by the researcher before the hypothesis test is carried out so they can’t pick something that will suit the result they want

51
Q

in the two tailed hypothesis test we are interested in finding convincing evidence that the population parameter is _____ to the null hypothesis value

A

different

52
Q

in a one tailed test, we are only interested in convincing evidence ________

A

in one direction

53
Q

the critical value marks a boundary in the distribution of possible test statistics if?

A

the null hypothesis is true

54
Q

a statistic beyond the critical value is deemed too unlikely if?

A

the null hypothesis is true so the null hypothesis is rejected

55
Q

in a two tailed test, there are ___ critical values and ___ rejection regions

A

2, 2

56
Q

in a one tailed test, there are ___ critical values and ___ rejection regions

A

1, 1

57
Q

if we reject the null hypothesis, we conclude that there is ________ at the specified level of ______ that _____

A

sufficient evidence, alpha, put alternative hypothesis in words

58
Q

if we do not reject the null hypothesis, we conclude that there is _____ at the specified level of ___ that _____

A

insufficient evidence, alpha, put the alternative hypothesis in words

59
Q

remember, a hypothesis test cannot?

A

prove a claim. just give sufficient or insufficient evidence

60
Q

what are the hypothesis testing steps

A 
Before data collection and analysis
	- State hypotheses
	- State significance level
Collect and analyse data
	- Compute test statistic
Decision
Make decision and hypothesis testing conclusion
61
Q

what are the requirements for a t test for a population mean

A

We need a random sample and either the population can be assumed to be approximately distributed or the sample size is large enough (greater than or equal to 30) for the sampling distribution of the sample mean to be approximately normally distributed if the population itself is not normal.

62
Q

how do you do a 2 tailed hypothesis test for a population mean

A
  1. Find the critical values using T.INV.2T in excel using the given alpha. These represent the boundaries of the rejection regions.
    1. Use this formula to work out the test statistic:
    2. If the test statistic is beyond the critical values (further into the tails) the decision will be to reject the null hypothesis
    3. Write the conclusion - mention whether or not there was sufficient evidence, mention the alpha value etc.
63
Q

what function do you use in excel for a 2 tailed hypothesis test

A

T.INV.2T

64
Q

what excel function do you use in excel for a one tailed hypothesis test

A

T.INV

65
Q

if the null hypothesis value is within the interval we would ?

A

not reject

66
Q

what is the z test for a population proportion requirements?

A

Random sample and the conditions for a binomial distribution are satisfied and we can expect at least 5 failures and 5 successes in our sample.

Critical values here use a standard normal distribution, so we use NORM.S.INV in excel to calculate the critical value. We then use the below formula to work out the test statistic and compare.

67
Q

what function do you use in excel for a z test

A

NORM.S.INV

stat101 (3 decks)

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