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- StudyBlue
- Mississippi
- Murrah High School
- Statistics
- Dilioglou
- AP Statistics

Tulante P.

Conditions for t

-Sample size less than 15. Use t procedures if the data are too close to normal. If the data are clearly nonnormal or if outliers are present, don't use t.

-Same size at least 15. The t procedures can be used except in the presence of outliers or strong skewness.

-Large samples. The t procedures can be used for clearly skewed distributions when the same is large, rougly n>40

Conditions for z

-Data comes from an SRS from the pop. of interest

-Sampling distribution of x-bar is approx. normal.

-Individual observations are independent. N>10n

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Mu *μ*

Population Mean

Two-Sided

Direction of the difference isn't specified. Ha:*μ=*0

One-sided

Null hypothesis says "no loss", alternative hypothesis says "there is a loss." Ho:μ=0 and Ha:μ>0. Interested only in deviations from the null hypothesis in one direction

σ(sigma)

Standard deviation of the population

σ_{X(sigma x-bar)}

Standard deviation of the sampling distribution

N

Population size

n

Sample size

z

The critical value for a confidence level c.

t

The critical value for a confidence level c. Number such that the area under the

t distribution for a given number of degrees of freedom falling between

c − t and c t is equal to c.

Toolbox for Confidence Interval

- Identify the pop. of interest & the parameter you want to draw conclusions about.
- Choose. the appropriate inference procedure. Verify the conditions for using the selected procedure.
- If the conditions are met, carry out the inference procedure. CI=estimate +-margin of error.
- Interpret your results in the contest of the problem.

Toolbox for Significance Test

- Identify the pop. of interest & the parameter you want to draw conclusions about. State null & alternative hypothesis in words & symbols.
- Choose the appropriate inference procedure. Verify the conditions for using the selected procedure.
- If the conditions are met, carry out the inference procedure. Calculate the test statistic. Find the P-value.
- Interpret your results in the context of the problem.

α (Alpha)

Type I error or Level of Significance.

P-value

The attained level of significance. P value is the smallest level of significance for which the observed sample statistic tells us to reject the null

hypothesis.

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C

Confidence interval level of the mean

m

Margin of error x-bar +-z* σ/ n

Ha

alternative hypothesis- the effect we suspect is true, the alternative to "no effect" or "no change".

Ho

H-nought. Indicate null hypothesis.

x-bar

Sample mean

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