Statistical Inference: Understanding Confidence Intervals and Hypothesis Testing, Quizzes of Statistics

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If p-value < (alpha)

Possible Type II Error Reject H Test is significant There is enough evidence to suggest a change, increase, etc. Strong evidence against the null Possible Type I Error TERM 2

If p-value > (alpha)

DEFINITION 2 Fail to reject H0 (but never accept it!) Test is insignificant There is insufficient evidence to suggest a change, increase, etc. No strong evidence against the null Possible Type II Error TERM 3

Point Estimate

DEFINITION 3 sample mean/proportion TERM 4

Confidence Interval for

Proportions

DEFINITION 4 point estimate+ confidence interval(z) * standard error TERM 5

Computing a Confidence Interval

DEFINITION 5 -first get point estimate-find margin of error- z* standard error- t* standard error- upper limit- point estimate- + or - point estimate from margin of error- ___% confident that population proportion/mean is in the interval

Properties of a C.I.

The sample proportion/mean is ALWAYS inside the confidence interval!- in the middleThe population proportion/mean may or may not be inside the confidence interval TERM 7

Interpretation of a C.I.

DEFINITION 7 We are 95% confident the population mean/proportion is somewhere inside the interval. The population mean, while unknown, is fixed What changes is the intervalIt is incorrect to say The population mean isin the confidence interval 95% of the time.A 95% C.I. also means that about 95% of all C.I.s constructed contain the true population proportion/mean, and about 5% do not TERM 8

Determining z

DEFINITION 8 95% C.I. : z = 1.96 (memorize) For others: use at least 5 decimalsP (z >= ?) TERM 9

Valid Confidence Interval for proportions

DEFINITION 9 Random sampleWe need np> 15 We need n(1-p) > TERM 10

Confidence level

DEFINITION 10 Increasing level of confidence (z) widens the intervalDecreasing level of confidence (z) shortens the interval

Sample size

Increasing the sample size shortens the C.I.Decreasing the sample size widens the C.I. TERM 12

Standard error

DEFINITION 12 Standard error decreases, so the margin of error (width) decreases as well TERM 13

Confidence Interval for Means

DEFINITION 13 point estimate+ confidence interval(t) * standard error TERM 14

Degrees of freedom

DEFINITION 14 n-1t-value changes as df changes TERM 15

Valid Confidence Interval for Means

DEFINITION 15 sampling should be from a normal populationn>

Confidence Intervals (StatCrunch) proportions

Stat > Proportions > One Sample > With Summary# Successes and # ObservationsC.I., level, Standard- Wald, CalculateTells you the C.I. and standard errorDoes not tell you the margin of error TERM 17

Confidence Intervals (StatCrunch) mean

DEFINITION 17 Stat > T-Statistics > One Sample > With DataSelect var1, NextC.I., level of confidence, calculateStat > T- Statistics > One Sample > With SummaryEnter sample mean, s.d., sample sizeC.I., level of confidence, calculate TERM 18

Sample size needed formula proportions

DEFINITION 18 n= p-hat(1-p-hat)*z squared/ margin of error squared TERM 19

Sample size needed formula mean

DEFINITION 19 n= standard deviation squared * z squared/ margin of error squared TERM 20

What do we choose for the sample

proportion?

DEFINITION 20 Proportion of a previous studyIf nothing is known, p =.

Hypothesis testing for

proportions

H0: p=p0Ha: p <,>,=/z=p-hat - p0 divided se TERM 22

Hypothesis testing for

means

DEFINITION 22 H0: m=m0Ha: m <,>, =/t= x-bar - m0 divided by se TERM 23

Assumptions for Testing proportions

DEFINITION 23 categorical datarandom samplesindependent samplesnp0> 15n(1-p0)> 15 TERM 24

Assumptions for Testing means

DEFINITION 24 quantitative variablerandom sampleindependent samplesn> 30population's normal TERM 25

Type 1 error

DEFINITION 25 reject the null when in fact you shouldnt have: it was actually the true conclusionConcluding the alternatives true when really the null is true

Type 2 error

fail to reject the null when in fact you should have: the alternative was the correct oneConcluding theres no sufficient evidence to contradict the null, when in fact the alternative is true