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ACC-Statistics > Exam 3 > Flashcards

Exam 3 Flashcards

1
Q

define Statistical Inference

A

Statistical inference is the process by which we acquire information and draw conclusions about populations from samples.

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2
Q

The objective of estimation is to determine the _________ _______ of a population parameter on the basis of a sample statistic.

A

The objective of estimation is to determine the approximate value of a population parameter on the basis of a sample statistic.

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3
Q

Define Point Estimator

A

A point estimator draws inferences about a population by estimating the value of an unknown parameter using a single value or point.

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4
Q

Define Interval Estimator

A

An interval estimator draws inferences about a population by estimating the value of an unknown parameter using an interval.

An alternative statement is:
The mean income is between 380 and 420 $/week.

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5
Q

Define Unbiased estimator

A

An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter.

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6
Q

An unbiased estimator is said to be _________ if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

A

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

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7
Q

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be _______ ________.

A

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

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8
Q

Interval Width
: A ______ interval provides little information.

A

Interval Width: 
A wide interval provides little information.

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9
Q

Increasing the sample size _______ the width of the confidence interval while the confidence level can remain unchanged.

A

Increasing the sample size decreases the width of the confidence interval while the confidence level can remain unchanged.

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10
Q

Error of estimation

A

We can define the sampling error as the difference between an estimator and a parameter. Specifically referred to as error of estimation

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11
Q

What is B mean and stand for in the sample size for proportion equation?

A

B in sample size for proportion equation is the maximum error of estimation that we are willing to tolerate, B stands for bound in the error of estimation.

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12
Q

The objective of estimation is to determine the approximate value of a population parameter on the basis of a ______ _________

A

The objective of estimation is to determine the approximate value of a population parameter on the basis of a sample statistic

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13
Q

That is we say (with some ___% certainty) that the __________ _________ of interest is between some lower and upper bounds.

A

That is we say (with some ___% certainty) that the population parameter of interest is between some lower and upper bounds.

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14
Q

The objective of estimation is to determine the approximate value of a _________ _________ on the basis of a sample statistic

A

The objective of estimation is to determine the approximate value of a population parameter on the basis of a sample statistic

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15
Q

what is Confidence Interval

A

It states that there is 1 - α probability that the sample mean will be equal to a value such that the interval

p(hat) plus or minus z alpha/2 sq rt ( p(hat) (1-p(hat)) / n )

will include the population proportion. Once the sample proportion is computed, the interval acts as the lower and upper limits of the interval estimate of the population proportion.

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16
Q

The probability 1 – α is the ________ ______, which is a measure of how frequently the interval will actually include p or µ.

A

The probability 1 – α is the confidence level, which is a measure of how frequently the interval will actually include p or µ.

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17
Q

Fail to reject null = ?

A

Fail to reject null = agreed with null hypothesis

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18
Q

Reject null = ?

A

Reject null = agreed with alternative hypothesis

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19
Q

What equation should you use:

Determine the sample size to estimate a population proportion within .02 with 99% confidence with p = .65

A

n = ( z α/2 sqrt(p(1-p)) / B ) ^2

Sample size for proportion Chapter 9

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20
Q

What equation should you use:
A marketing manager wanted to know whether his new product design was going to be popular. He asked a random sample of 500 potential customers whether they liked the new design better than the current design. A total of 320 people said that they did. Estimate with a 95% confidence the proportion of all potential customers who would prefer the new design.

A

P(hat)= x / n
p(hat) plus or minus z alpha/2 sq rt ( p(hat) (1-p(hat)) / n )

Sample proportion and confidence interval for the proportion

Chapter 9

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21
Q

A ____ ___ ____ occurs when we reject a true null hypothesis. That is, a ____ ___ ____ occurs when the jury convicts an innocent person.

A

A Type I error occurs when we reject a true null hypothesis. That is, a Type I error occurs when the jury convicts an innocent person.

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22
Q

A ____ ___ ____ occurs when we don’t reject a false null hypothesis. That is, a ____ ___ ____ occurs when a guilty defendant is acquitted, let go.

A

A Type II error occurs when we don’t reject a false null hypothesis. That occurs when a guilty defendant is acquitted, let go.

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23
Q

What is a hypothesis

A

A hypothesis is a claim (assertion) about
a population parameter:

population mean

Ex: The mean monthly cell bill in city is µ = $42

population proportion

Ex: The proportion of adults in this city with cells is p = 0.68

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24
Q

H0: — the ‘null’ hypothesis always uses what symbols

A

equals, greater or equal to, less than or equal to

“=” , “≤” or “≥” sign

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25
Q

H1: — the ‘________’ or ‘________’ hypothesis

A

H1: — the ‘alternative’ or ‘research’ hypothesis

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26
Q

What is the alternative Hypothesis?

A

Is the opposite of the null hypothesis
e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: μ ≠ 3 )
Challenges the status quo
Never contains the “=” , “≤” or “≥” sign
May or may not be proven
Is generally the hypothesis that the researcher is trying to prove

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27
Q

P(Type I error) = ?

A

P(Type I error) = α

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28
Q

P(Type II error) = ?

A

P(Type II error) = β

29
Q

two possible errors

A

Type I error: Reject a true null hypothesis

Type II error: Do not reject a false null hypothesis.

30
Q

α is called the ___________ _____

Set by researcher in advance

A

α is called the significance level

Set by researcher in advance

31
Q

What are critical values

A

Critical values are what define the rejection region, There are two cutoff values (critical values), defining the regions of rejection

32
Q

Two-tail test

A

rejection region is in both tails, non directional, α / 2

33
Q

what are the six-steps to hypothesis testing

A

State the appropriate null and alternative hypotheses
H0: μ = 3 H1: μ ≠ 3 (This is a two-tail test)
2. Specify the desired level of significance and the sample size
Suppose that α = 0.05 and n = 100 are chosen for this test
3. Determine the critical values
For α = 0.05 the critical Z values are ±1.96
4. Collect the data and compute the test statistic
Suppose the sample results are
n = 100, X-bar = 2.84 (σ = 0.8 is assumed known) [Zstat Equation]
5. Is the test statistic in the rejection region? [Graph]
6. Reach a decision and interpret the result

34
Q

What is P-value hypothesis testing

A

p-value: Probability of obtaining a test statistic equal to or more extreme than the observed sample value given H0 is true
The p-value is also called the observed level of significance
It is the smallest value of α for which H0 can be rejected

35
Q

If the p-value is ___ then H0 must go

A

low

36
Q

_________________ H0 since p-value = 0.0136 < α = 0.05

A

Reject H0 since p-value = 0.0136 < α = 0.05

37
Q

Use which equation to find test statistic

A

Zstat

38
Q

Which equation should you use:
Has the recent drop in airplane passengers resulted in better on-time performance? Before the recent downturn one airline bragged that 92% of its flights were on-time. Can we conclude at the 5% significance level that the airline’s on-time performance has improved?

A

p(hat) and Zstat

Zstat = (p(hat) - p) / (sq rt(p(1-p)/n))

Chapter 10 One-Tailed

39
Q

Critical values you _____

A

critical values you lookup

40
Q

test statistics you ______

A

Test statistics you calculate

41
Q 
Which equations should you use:
The university of Memphis advertises that its average class size is 35 students or less.  A student organization is concerned that budget cuts have let to increased class sizes and would like to test this claim.  A sample of 38 classes were selected and the average class size is 36.9 students.  The standard deviation for the entire college is 8 students.  Using an alpha = .05, does the student have enough evidence to show that class sizes have increased?
A

Six Step Method, One-Tailed, Zstat Sigma known

42
Q

What is degrees of freedom

A

Number of observations that are free to vary after sample mean has been calculated (ν = n – 1)

43
Q

Degrees of freedom = ?

A

Degrees of freedom = n - 1

44
Q

tstat < - tcrit or tstat > tcrit

A

Reject

45
Q

Interested in a population’s central location: It has a Z-Distribution so we use a Z-test statistic when the Sigma Squared is ________

A

Interested in a population’s central location: It has a Z-Distribution so we use a Z-test statistic when the Sigma Squared is known

46
Q

Interested in a population’s central location: It has a t-Distribution so we use a t-test statistic when the Sigma Squared is ________

A

Interested in a population’s central location: It has a t-Distribution so we use a t-test statistic when the Sigma Squared is unknown

47
Q

How to read the t-table

A

(over) Upper tail area = alpha/2

(down) degrees of freedom = n-1

48
Q

If we are interested in drawing inferences about a population’s variability, we investigate population variance: σ^2 using ______ _________

A

If we are interested in drawing inferences about a population’s variability, we investigate population variance: σ^2 using sample variance (s^2)

49
Q

If we are interested in drawing inferences about a population’s variability, It has a chi-squared distribution so we use a ___ _______ ________, with n–1 degrees of freedom.

A

If we are interested in drawing inferences about a population’s variability, It has a chi-squared distribution so we use a χ2 test statistic, with n–1 degrees of freedom.

50
Q

when comparing two populations, we examined ___________ __________

A

when comparing two populations, we examined independent samples.

51
Q

If, however, an observation in one sample is matched with an observation in a second sample, this is called a ________ _____ __________.

A

If, however, an observation in one sample is matched with an observation in a second sample, this is called a matched pairs experiment.

52
Q

what is the F test used for

A

to compare two population variances

53
Q

What is the equation for testing a population means, with equal variances?

A

t = ( (xbar1-xbar2) - (mu1-mu2) ) / ( sqrt(Sp^2(1/n1+1/n2) )

54
Q

What is the degree of freedom for an F test?

A

V1 = n1-1 and V2 = n2-1

55
Q

What is the equation for pooled variance

A

Sp^2 = ( (n-1) s1^2 + (n2-1) s2^2 ) / ( n1+n2-2 )

56
Q

How to read the F Table

A

numerator degrees of freedom determine the column

denominator degrees of freedom determine the row

57
Q

T/F? If a sample has 25 observations and we need a 95% confidence estimate for the population mean with an unknown standard deviation, the appropriate value of t is 2.064.

A

true

58
Q

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?
Question options:

a) The population random variable must be normal.
b) The test statistic must be a non-negative number.
c) The test statistic must have a chi-squared distribution with n - 1 degrees of freedom.
d) All of these choices are true.

A

d) all of these choices are true

59
Q

Researchers determined that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 96 persons yielded the following data on the number of tissues used during a cold: sample mean x-bar= 52 and s = 22. Suppose the alternative we wanted to test was H1: m 1.661

b) Reject H0, if t 1.985 or Z

A

b) Reject H0, if t

60
Q

T/F? the lower limit of 90% confidence interval for the population proportion p, given that n = 400 and the sample proportion p-hat=.10, is .0247

A

False

61
Q

T/F? Increasing the probability of a Type I error will increase the probability of a Type II error

A

False

62
Q

T/F? The statement of the null hypothesis always includes an equals sign

A

True

63
Q

What would be an appropriate alternative hypothesis?

A

The population mean is not equal to 40

INCORRECT:
The sample mean is equal to 40
The population mean is equal to 40
The sample mean is not equal to 40

64
Q

T/F? Reject H0, when Zstat < - Zcritical

A

True

65
Q

T/F? Reject H0, when Zstat < Zcritical

A

False

66
Q

T/F? Reject H0, when Zstat > - Zcritical

A

False

67
Q

T/F? Reject H1, when Zstat < - Zcritical

A

False

68
Q

If the p-value is < alpha, then

a) you fail to reject the null hypothesis
b) reject the null hypothesis

A

if the p-value is low, it must go.

b

ACC-Statistics (4 decks)

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