Flashcards
CHAPTER 8,9,10
Cards in this deck (52)
- 1Point Estimatorstatistic that provides an estimate of a population parameter.
- 2Point Estimatevalue of the statistic from the sample
- 3Standard deviation of a sampleox=o/sqrt(n)
- 4Center of a confidence intervalux=u, or the mean of the sampling distribution is the same as the unkown population
- 5C% confidence intervalgives an interval of plausible values for the parameter.
point estimate +/- margin of error - 6Margin of errorthe difference between the point estimate and the true parameter value will be less than the margin of error in C% of samples
- 7Confidence leveloverall success rate of the method for calculating the confidence interval
- 8Interpreting Confidence intervals"We are C% confident that the interval from ___ to ___ captures the [parameter we are trying to find in context]"
- 9Interpreting confidence levels"If we take many samples of the same size from this population, about C% of them will result in an interval that captures the actual parameter."
- 10What does the confidence interval tell you?The chance of how likely it is the method will produce an interval that captures the population parameter.
- 11Calculating a confidence intervalstatistic +/- (critical value)(which is the z or t score)*(standard deviation of the statistic)
- 12Calculating the margin of error(critical value)*(standard deviation of the statistic)
- 13Conditions for Estimating PRandom
10% Rule-n/=10,
n(1-p)>/=10 - 14What happens if the conditions are violated?You can't complete the interval
- 15Standard errorSqrt(p(1-p)/n)
- 16Standard error definitionWhen the standard deviation of a statistic is estimated from the data
- 17Standard deviation of the sampling distributiono=sqrt(p(1-p)/n)
- 18Z Interval for a population proportionp(hat)+/-z*standard deviation of the statistic)
- 19SPDC for Confidence IntervalsState:What is the parameter do you want to estimate, and at what confidence level?
Plan: Identify the appropriate inference method. Check conditions
Do: If the conditions are met, perform the calculations(write what type of test you are using)
Conclude: Interpret the interval in context of the problem - 20Choosing Sample SizeThe margin of error is largest when p is equal to .5 so when p is unknown use .5
To solve for n>/=(z/ME)^2*(p)*(1-p) - 21The margin of error formulaz*sqrt(p*(1-p)/n)
- 22When o is unknownFor population proportion it is x+/- z*sx/sqrt(n)
To solve for t=x-u/sx/sqt(n)
To solve for z=x-u/o/sqrt(n) - 23Degrees of freedomn-1
- 24Conditions for a t intervalrandom
10%-n/=30 or Normal or approximately normal - 25Standard error of the sample meanSE=sx/sqrt(n)
- 26Choosing a sample size when estimating uz*o/sqrt(n)
- 27Null HypothesisHo or no difference
- 28Alternative HypothesisHa, difference , can be less than, greater than, or not equal to
- 29How do you know whether it is greater than / smaller than or equalOne sided: larger than or smaller than
Two sided or not equal to: parameter is different from null - 30P ValueThe probability that the null os true
- 31Statistically significant at level alphaIf the P value is smaller than alpha, we say the results are statistically significant at level alpha. In that case, we reject the null hypothesis and conclude that there is convincing evidence in favor of the alternative
- 32Significantnot likely to happen by chance
- 33Type I errorIf we reject the null when the null is true, we have committed a Type 1 error
- 34Type II errorIf we fail to reject the null when the alternative is true
- 35What is the probability of a Type I error?The significance level of any test
- 36Test Statisticstatistic-parameter/standard deviation of statistic
- 37Significance Tests SPDCState: What is the hypothesis, and at what significance level? Define the parameters you used
Plan: Choose the appropriate inference method. Check conditions
Do: If the conditions are met perfrm the calculations also write what test you are using
Conclude: Make a decision on the hypothesis - 38Z Statistic formulaz=p(hat)-P/sqrt(p*(1-p)/n)
- 39Powerprobability that the test will reject the null at the significance level when Ha is true
- 40Power formula1-Beta
- 41How to increase the power of a significance testIncrease sample size
Increase the significance level
Increase the difference between the null and the alternative parameter values that are important to detect - 42Paired dataUses a one sample t test
- 43Comparing Two ProportionsShape:n1*p1>/=10 n2*p2>/=10 approximately normal
Center: u1=p1 and u2=p2
Spread: op1=sqrt(p1(1-p)/n1) and op2=sqrt(p2(1-p2)/n2) - 44Sampling distribution of p1-p2Shape: When n1*p1, n1*(1-p1), n2*p2, and n2(1-p2) >=10 then the shape is approximately normal unless both shapes of the graphs are normal
Center: p1-p2
Spread: sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2)
As long as n - 45Conditions for a two sample confidence intervalRandom: both samples are random
10%- n1 <=1/10N
n2<=1/10N
Large Counts: n1*p1, n1*(1-p1), n2*p2, and n2(1-p2) >=10 - 46Confidence interval of difference between two proportions(p1-p2) +/- z* standard devaition
- 47Null hypothesis in two sample testp1-p2=0 or p1=p2
- 48Pooled or combined sample proportionx1+x2/n1+n2
- 49z test statistic(p1-p2)-0/sqrt(pc(1-pc)/n1+pc(1-pc)n2)
- 50two sample t test standard deviationox1-x2=sqrt(o1^2/n1+o2^2/n2)
- 51degrees of freedom(s1^2/n1+s2^2/n2)^2/1-n1-1(s1^2/n1)^2+1/n2-1(s2^2/n2)^2
- 52Standard error of two sample meansqrt(s1^2/n1+s2^2/n2)
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- 11th grade Statistics Flashcards on CHAPTER 8,9,10, created by Arieanna Nazir on 13/04/2019.
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