z , t, chi square & F test

1. STAT TESTS
Z TEST, T TEST & CHI SQUARE TEST
Presented by: Pinaki Ranjan
Brahma

2. Z TEST
We want to estimate the average weight for the adult male population. The
average weight of 100 randomly selected adult males is 180 lbs. Assume a
population standard deviation of 20 lbs. Compute a 95% confidence interval
for the population average weight.
• Population mean = sample mean +/- sample error
• µ = Xavg +/- (z x σ)/ √(n)
• z is found from z table  1.96
• degrees of freedom = 100-1 = 99
• α = (1 - 95%)/2 = 0.05 /2 = 0.025 → 0.9750
• µ = (176.08, 183.92)

3. Z TABLE FOR FINDING THE CRITICAL VALUE

4. T TEST
The test scores of 9 randomly selected students are:
83, 73, 62, 63, 71, 77, 77, 59, 92 Compute the 99% confidence
interval of the true mean
• Population mean = sample mean+/- sample error
• µ = Xavg +/- (t x s)/ √(n)
• t is found from t table  1.96
• degrees of freedom = 9-1 = 8
• α = (1 - 99%)/2 = 0.01 /2 = 0.05
• µ = (61.04, 84.95)
We go for t test only when
1. Population std dev is
unknown
2. Sample size < 30

5. T TABLE FOR FINDING THE CRITICAL VALUE

6. CHI SQUARE TEST
H0: Die is fair
Halt: Die is unfair
• Ӽ2
stat = ∑(xobs – xexp)2/xexp
= 15.29
• Ӽ2
crit = 15.086
• degrees of freedom = 6-1 = 5
• α = (1 - 99%)/2 = 0.01 /2 =
0.05
• Compare Ӽ2
stat with Ӽ2
crit
• Since Ӽ2
stat > Ӽ2
crit
• H0 is rejected  Die is
unfair
# 1 2 3 4 5 6 Tot
al
freq 22 24 38 30 46 44 204
# 1 2 3 4 5 6 Tot
al
freq 34 34 34 34 34 34 204
ObservedExpected
= 204 x
(1/6)
0.0
5
15.086
15.29
How good an Observed
data fits the Expected
data

7. CHI SQUARE TABLE FOR FINDING THE CRITICAL
VALUE

8. F TEST
Does at least one parameter
significantly impact the
dependent variable