{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Hypothesis_Testing_t_testing_lecture

# Hypothesis_Testing_t_testing_lecture - Hypothesis Testing...

This preview shows pages 1–4. Sign up to view the full content.

Hypothesis Testing, σ Unknown Case I: 1. The population has any distribution 2. The sample size is large (n 30) 3. σ is unknown. Since n is large, the value of σ is approximated by the sample standard deviation s. _ Χ - μ z = ------------- s n Case II: 1. The population is normally distributed 2. The sample size n is small. 3. σ is unknown. USE t-test __ Χ - μ t = ------------ s n degree of freedom ν = n – 1 Use Table 5 t-distribution table Example: 1. 2-tailed test, α = 0.05, ν = 6 t c = 2.447 2. 2-tailed test, α = 0.01, ν = 12 t c = 3.055 3. one-tailed test, α = 0.05, ν = 7 t c = 1.895 4. one-tailed test, α = 0.01, ν = 11 t c = 2.718 t c critical t value

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hypothesis testing, σ unknown Examples: 1. Experience has shown that the number of matches in boxes follow a normal distribution. A manufacturer claims that the average number of matches in its boxes is 50. A customer purchases a random sample of 9 boxes and counts the contents of each box. They were: 49 50 51 46 48 45 52 47 48 Based on this sample, should the customer believe the manufacturer’s claim? Use 2-tailed test, α = 0.05. μ = 50 μ is the standard mean, the one that we want to test. n = 9, so ν = n – 1 = 8 s = calculate standard deviation of the sample data = use s x of your Sharp calculator or σ n-1 of your Casio calculator. s = 2.29 X (mean) = 48.4 H 0 : μ = 50 H 1 : μ 50 this makes our test 2-tailed α = 0.05, ν = 8 t c = 2.306 our computed t value should be within range –2.306 t 2.306 Χ - μ 48.4 - 50 t = ------------ = --------------- = -2.03 s 2.29 n 9 Since –2.03 is within the range –2.306 t 2.306, retain H 0 Therefore, the number of matches per box remains at 50.
2. The number of errors on the pages of a statistics textbook follows a normal

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

Hypothesis_Testing_t_testing_lecture - Hypothesis Testing...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online