T-Tests and Chi2. Does your sample data reflect the population from which it is drawn from?. Single Group Z and T-Tests.
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T-Tests and Chi2
Does your sample data reflect the population from which it is drawn from?
For α =.05 and N=30 , t =2.045
20± 2.086 (5/19) =
For example, we can take a random set of independent voters who have not made up their minds about who to vote for in the 2004 election. But we have another suspicion:
H1: watching campaign commercials increases consumption of Twinkies (snackie cakes), or μ1≠ μ2
Null is μ1= μ2
After one group watches the commercials, but not the other, we measure Twinkie in-take. We find that indeed the group exposed to political commercials indeed ate more Twinkies. We thus conclude that political advertising leads to obesity.
Two Sample Difference of Means T-Test
Pooled variance of the two groups
= common standard deviation of two groups
Females: mean = 50.9, variance = 47.553, n=6
Males: mean=41.5, variance= 49.544, n=10
Now what do we do with this obtained value?
The critical values are set by moving toward the tails of the distribution. The higher the significance threshold, the more space under the tail.
Also, hypothesis testing can entail a one or two-tailed test, depending on if a hypothesis is directional (increase/decrease) in nature.
Obtained Value: 2.605
Degrees of Freedom: number of cases left after subtracting 1 for each sample.
Is the null hypothesis supported?
Answer: Indeed, women have higher verbal skills and this is statistically significant. This means that the mean scores of each gender as a population are different.
ΣD = sum differences between groups, plus it is squared.
n = number of paired groups
H0: μ scr1 = μscr2 whereas research hypothesis H1:
Given the sample size, how many cases could we expect in each category (n/#categories)? The obtained/critical value estimation will provide a coefficient and a Pr. that the results are random.