Final Module (6 & 7) Flashcards
2-tailed test hypothesis test
H0: 𝑋 = 𝜇
Ha: 𝑋 ≠ 𝜇
1-tailed test hypothesis test
H0: 𝑋 = 𝜇
Ha: 𝑋 > 𝜇 OR Ha: 𝑋 < 𝜇
Z-score
measures how many standard deviations away from the mean your measurement is
𝑧 = 𝑋 − 𝜇 / 𝜎
Significance level (𝛼)
percentage of the data you want to be above or below you measurement in order for it to be significantly different from the mean
(most often: 𝛼 = 5%)
Confidence level equation
1 - 𝛼
p-value
the area of the tail beyond your measurement
- the probability of obtaining the value as extreme or more extreme as the given value, provided that H0 is true
How to Calculate the p-value?
1) Z-table or T-table
2) Excel using 1- normal or 1- standard normal dist
𝑝 ≤ 𝛼
reject H0, your value is significantly different from the mean
𝑝 > 𝛼
fail to reject H0
Sample mean is a random variable with
standard deviation, this is called standard error
Assumptions of Z-test
(What if not all of these assumptions are met?)
- Sample data follow a normal distribution
- All observations are independent
- Sample size is more than 30
- Population standard deviation is known
If these are not met then use a t-test
Types of two samples
- well-separated distributions
- overlapping distributions
- different variances
The confidence interval of two samples
𝑋 ± 𝑡-critical * 𝑠 /√𝑛
Hypothesis Tests for Variances
- Hypothesis test for single variance – use 𝜒2 distribution
- Hypothesis test for equality of two variances – use F-distribution
𝝌𝟐 (chi-squared) distribution
distribution of the sum of 𝑘 independent standard normal random variables