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.