**Hypothesis Testing**

- Null Hypothesis: H
_{0}

Â - Alternative Hypothesis: Ha

Â - Confidence Intervals (CI)

Â - Hypothesis Tests for Variances:

Â

oÂ Â Tests for a Single Population Variances

Chi-Square test

Â

H0: Ïƒ2 = cÂ

Â Â Â Â Â Â Â Â Â Â Â Â

Â HA: Ïƒ2 â‰ cÂ

Â

Â

Â

oÂ Â Tests for a two Population Variances:

**Â **

F test

H0: Ïƒ12 â€“ Ïƒ22 = 0

Â

HA: Ïƒ12 â€“ Ïƒ22 â‰ 0

**Â **

- Â One Tailed Test:

Test if the value is greater than or less than K

H_{0}; Âµ<=K vs. H_{a}: Âµ>K

- Two Tailed Test:

Test if the value is different from K

H_{0}; Âµ=0 vs. H_{a}: Âµâ‰ 0

Â

**Sample Question**

Question:

Question:

Â

If standard deviation of a normal population is known to be 10 & the mean is hypothesized to be 8. Suppose a sample size of 100 is considered. What is the range of sample means in which hypothesis can be accepted at significance level of 0.05?

Â

**Ans:**

SE = 10/âˆš100 =1

Â

z = (x-Âµ)/ SEÂ Â Â = (x-8)/1

Â

At 95% -1.96

Therefore 6.04

Â

Â

Â

Â

Â

Â