Chpt 9

True or false? Compared to a z-score, a hypothesis test with a t statistic requires less information about the population.

True. The t statistic does not require the population standard deviation; the z-test does.

Hypothesis should be accompanied by what?

a measure of effect size.

Hypothesis test determines whether the treatment effect is greater than _______?

chance. -No measure of the size of the effect is included. -A very small treatment effect can be statistically significant.

When n is small (less than 30), the t distribution _________

is flatter and more spread out than the normal z distribution.

Degrees of freedom

n-1

Z-score statistic

z= M-u/0~m

Sample Variance and SD

𝑠^2=(Σ(𝑋−𝜇)^2)/(𝑛−1)=(Σ𝛿^2 )/(𝑛−1) 𝑠=√(𝑠^2 )=√((Σ(𝑋−𝜇)^2)/(𝑛−1))

Population Variance and SD

𝜎^2=(Σ(𝑋−𝜇)^2)/𝑁=(Σ𝛿^2 )/𝑁 𝜎=√(𝜎^2 )=√((Σ(𝑋−𝜇)^2)/𝑁)

Cohen's d

-Original equation included population parameters. -estimated cohen's d is computed using the sample standard deviation. Estimated d= mean difference/sample standard deviation(m-u/s)

Estimated standard error

-Uses s2 to estimate o~2 Sm = s/sqroot of n

The t-statistic

-Uses the estimated standard error in place of O~m t = M - u/Sm -used a test hypotheses about an unknown population mean 'u' when the value of 0~ is also unknown

t-distribution

-one for each value of degrees of freedom -Approximates the shape of the normal distribution *Flatter *more spread out *"fatter tails" -Use table of Values of t in place of the Unit Normal Table for hypothesis tests

Standard error

0~m = 0~/SQROOT of sample size (n)

Hypothesis testing steps

1. state the null and alternative hypotheses and select an alpha level. 2. locate the critical regain using the t distribution table and df 3.Calculate the t test statistic 4.Make a decision regarding Ho (null hypothesis)

____ ______ ______ is used as in place of the real standard error when the value of 0~m is unknown.

Estimated standard error (Sm)

True or false? By chance, two samples sleected from the sample population have the same size (n = 36) and the same mean (M = 83). That means they will also have the same t statistic.

False. The teo t values are unlikely to be the same; variance estimates (s2) differ between samples.