11_04_2004 Quantitative

Paper reviews Wednesday 1, 2, 3 o'clock.

Practice case 1a:

Null hypothesis – all our high school seniors mean will be 500

Alternative hypothesis: our mu will NOT be 500.

If s.e.m. is 3.16 (100/31.6 -- sigma/sq.root of sample size = sample error of mean)

Sample Distribution of the mean – the theoretical distribution of the means for an infinite number of samples

Zx (Z is sample mean) = -11

convert –11 points into standard error values - -11/3.16 = -3.4 s.e.m. below hypothesized mu

Look at table to see what % likelihood this would be and make likely/unlikely determination from that.

CRITICAL VALUE: Gives us the fence.

"z-observed" – tables, tells you where the "fence" is.

Don't use the word "significant" when writing about quant work UNLESS you mean STATISTICALLY significant.

T-testing, same logic as z-testing, just different tables, slightly different logic.

sample MUST be normally distributed for z or t test.

T-test are for instances where mu is NOT known.

Measure a sample of individuals on a variable of interest/variables of interest

and Compare to a population parameter

Identify pop of interest (students receiving new algebra curriculum)

Ho mu = 503

Ha mu is not = 503

select level of significance (.05, .01)

Draw sampling distribution of mean if mu = 503 – looks like normal ? For z distribution. When we talk about other distributions we look at something different – a t-distribution, not quite normal. Higher sample sizes are closer to normal.

Degrees of freedom (df)

How many standard errors is 530 away from 503 =27.

104/sq root of 64 (8) = 13s.e.

27/13=

2.08

Our sample mean was 2.08 standard errors away from our hypothesized mean, which is greater than the critical number of standard errors required to rejec the null hypothesis.

T-critical value is the "fence"

T-observed value is the # of s.e. our sigma differs from our mu in standard error units