Flashcards in Stat - Exam #2 Deck (90)

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31

## What are the Estimators for population parameters?

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Location = Mean, Median, Mode

Spread = Standard Deviation, Range, IQR

32

## What are the properties of a good estimator?

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1. Unbiased = expected value of estimator equals value of parameter;

2. Consistent = larger sample makes estimator more accurate;

3. Efficient = estimator has the smallest standard deviation

33

## What is a Confidence Interval Estimate?

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Range of values if an interval on the real number line;

-Expresses the natural uncertainty in the estimate

34

## What is a Confidence Level?

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The proportion of confidence intervals calculated from a large number of random samples that contain the value of the population parameter

Denoted = CL;

Common Values = 90%, 95%, 99%;

Decided by the researcher

35

## What is the Significance Level?

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The area outside of the region of confidence;

Denoted = sigma

Calculated = {1 - (CL/100)}

36

## What is a Critical Value?

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The pair of values that bound the region of confidence

Denoted = (+/- z_alpha/2’), (+/- t_alpha/2, n-1)

37

## What is the Confidence Interval Estimate of a Population Parameter of a Population when Standard Deviation is KNOWN?

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-An estimate of the value of a population parameter consisting of

1. an interval of number, and

2. a level of confidence that the interval contains the value of the population parameter

Denoted = CI% = (LCL,UCL)

LCL — Lower Confidence Limit; UCL — Upper Confidence Limit

38

## What determines the WIDTH of the confidence interval?

### Comes from the confidence level CHOSEN and the spread of the sample average

39

## What is given by the confidence level?

### Gives the area in the RIGHT tail (alpha/2), which gives the critical values bounding the region of confidence (+/-z_alpha/2)

40

## Where does the CENTER of the confidence interval come from?

### The CENTER of the confidence interval comes from the value of the SAMPLE AVERAGE (x-bar)

41

## What are the steps of a Confidence Interval?

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1. First find the critical values — defines the width of the interval (which is centered around the population mean, which is unknown)

2. Need to slide the interval over until it is centered on the sample average, which is known;

3. Convert the critical values into x-values;

4. Two x-values in the proper from make the confidence interval

42

## What is the Margin of Error?

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The RIGHT term in a confidence interval estimate;

-Determined the width of the confidence interval;

-Anything that changes the margin of error changes the width of the confidence interval

Margin = {z_(alpha/2)} x {sigma/(sq. rt of n)}

43

## What happens with a REDUCED margin of error?

### NARROWS confidence interval

44

## What happens with an INCREASED margin of error?

### WIDENED confidence interval

45

## What are the 3 ways to change the Margin of Error?

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1. Sample size: Increase = Narrow; Decrease = Widen;

2. Confidence level: Increase = Widen; Decrease = Narrow;

3. Standar deviation of the population: IMPOSSIBLE to change

46

##
What is the method for the Confidence Interval Estimate (z) of the Population Mean?

(Pop. SD is KNOWN)

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1. Statistics = Sample Average (x-bar) & Population Standard Deviation (sigma);

2. Critical Value = Confidence Level (CL) & Critical Z-score (z_sigma/2);

3. Compute = CI% = {x-bar +/- (z_alpha/2) (sigma/sqrt. n)}

4. State = CI% = (LCL, UCL)

47

## How is calculating confidence intervals estimates different when the population standard deviation is NOT known?

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-Use the sample standard deviation (which can always be calculated) to calculate confidence interval estimates of a population parameter;

-Major difference is is the the DEGREES of FREEDOM must be known and must use the t-table to get critical values

48

##
What is the method for the Confidence Interval Estimate (t) of the Population Mean?

(Pop. SD is NOT known)

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1. Statistics = Sample Average (x-bar) & SAMPLE Standard Deviation (s);

2. Critical Value = Confidence Level (CL), Degrees of Freedom (n-1) & Critical t-value {t_(alpha/2), (n-1)};

3. Compute = CI% = {x-bar +/- {t_(alpha/2), (n-1)} x [s/sqrt. n)]}

4. State = CI% = (LCL, UCL)

49

## What is a Hypothesis Test?

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1. First write 2 statement about a population parameter;

— Status quo value of the population parameter is given in the first statement;

— Claim made by the researcher is given in the second statement;

2. Sample data are collected and analyzed;

3. Finally concluded which statement is closer to the truth

50

## How is a hypothesis test different from a confident interval calculation?

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With a hypothesis test, you first must make some claim about a population parameter;

-Then collected data and determine if the claim is reasonable or not

51

## What are the 3 steps of a hypothesis test?

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1. Hypothesize = a set of hypotheses are written giving the status quo and the researchers claim;

2. Analyze = sample data are collected and analyzed;

3. Conclude = a conclusion as to which statement is closer to the truth is made

52

## What is a hypothesis?

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A statement about a population parameter;

EX: u=50 (pop mean)

- Can be for one or more populations

- Must be about the value of a population parameter (never a sample stat)

- Made BEFORE data is collected — and sample must be appropriate to the the statement;

**Two Types = Null and Alternative Hypothesis

53

## What is a Null Hypothesis?

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A statement that the population parameter has the status quo value;

- Denoted = “H-naught” (H0);

- EX = H0 : u = 72;

- Assumed TRUE in the hypothesis test until the sample evidence proves OTHERWISE;

-ALWAYS contains an EQUAL SIGN

54

## What is an Alternative Hypothesis?

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-A statement that a population parameter does NOT have the status quo value;

**Gives the researchers CLAIM;

- Denoted = “H-one” (H1);

- EX = H1 : u /= 72, H1 : u 72;

- Assumed FALSE in the hypothesis test until the sample evidence proves otherwise;

-NEVER contains an EQUAL SIGN

55

## What is the purpose of analysis of a hypothesis test?

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-Decide which hypothesis is closer to the truth, the null hypothesis or the alternative hypothesis;

-3 scenarios for a hypothesis test =

1. z-Test of the Mean

2. t-Test of the Mean

3. z-Test of Proportion

56

## What are the 3 methods in each scenario to conduct a hypothesis test?

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1. Critical Value Method = Traditional

2. P-value Method = Modern

3. Confidence Interval Method = Two-Sided

57

## What is the conclusion to a hypothesis?

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-Must chose only one of the two conclusions to end a hypothesis test;

1. REJECT the null hypothesis, or

2. NOT REJECT the null hypothesis

*Never enough information to prove a hypothesis is true, so a hypothesis can be shown to be false or not false — never shown true

58

## What is Hypothesis Testing?

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A producer that uses our knowledge of probability with evidence from a sample to test a claim about a characteristic of a population;

— Claim is about the value of a population parameter;

— Can be for one or more populations

59

## What are the Assumptions of Hypothesis Testing?

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1. Simple random sample;

2. Sample average is normally distributed

60