Bài giảng tối ưu hóa Bài 3 Ttest (phần 2) Ph.D Lê Minh Tâm

Preliminary step: checking assumptions... Define null and alternative hypotheses two-sided lower, one-sided greater, one-sided Research question: Whether the mean level of Salmonella i

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William Sealy Gosset (1876 - 1937)

Thicker tails and larger standard deviation

when df is large, the curve approaches the normal distribution

The reason for that is: when n is increased, the estimated

standard error will not fluctuate as much between samples

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Preliminary step: checking assumptions

1 Define null and alternative hypotheses

(two-sided) (lower, one-sided) ( greater, one-sided)

Research question:

Whether the mean level of Salmonella is greater than 0.3 ?

Null hypothesis Alter hypothesis

2 Set the criterion:

0.05

9 – 1 = 8

One sided test

3 Collect sample data

1 2 3 4 5 6 7 8 9 0.593 0.142 0.329 0.691 0.231 0.793 0.519 0.392 0.418

4 Calculate t-statistics

4 Calculate t-statistics

1 2 3 4 5 6 7 8 9 0.593 0.142 0.329 0.691 0.231 0.793 0.519 0.392 0.418

Preliminary step: checking assumptions

Assumptions

Checking assumptions

Checking assumptions

Checking assumptions

Checking assumptions

Checking assumptions

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Electric solution Chemical solution

Research question

Do electric solution and chemical solution differ

in terms of their effect ?

2 Population frequency distribution

Sampling distribution of

Sampling distribution

of

Preliminary step: checking assumptions

1 Define null and alternative hypotheses

Null hypothesis Alter hypothesis

Research question

Do electric solution and chemical solution differ in

terms of their effect ?

2 Set the criterion:

0.05 (12 – 1) + (12 - 1) = 22 Two-sided

Exp Electric Chemical

Do electric solution and chemical

solution differ in terms of their effect ?

3 Collect sample data

4 Calculate t-statistic

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5 Interpret results

Preliminary step: checking assumptions

Assumptions

Assumptions

Checking assumptions

Checking assumptions

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4 Calculate t-statistic

̅ ̅

4 Calculate t-statistic

̅ ̅

https://www.youtube.com/watch?v=kvmSAXhX9Hs&list=PLqzoL9-eJTNBDdKgJgJzaQcY6OXmsXAHU&index=29

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Research question: Does alcohol affect a

person’s ability to drive ?

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Preliminary step: checking assumptions

1 Define null and alternative hypotheses

2 Set the criterion

df =

α =

3 Collect sample data

4 Calculate t-statistic

Preliminary step: checking assumptions

Assumptions

Checking assumptions

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• To test hypotheses about

when the population

standard deviation is known

• Condition: population

distribution is normal or

sample size is large

Z-test / Z-statistic

when the population standard

distribution is normal, but

The z-test assumes that:

• The numerator varies from one

sample to another

• The denominator is constant

(from one sample to another)

The t-test assumes that:

• The numerator varies from one sample to another

• The denominator varies from one sample to another

The sampling distribution of z derives

from the sampling distribution of the

mean

The sampling distribution of t is broader than the sampling distribution

of the mean The sampling distribution of t changes with degree of freedom

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• The population standard deviation: (unknown)

• The sample standard deviation: (known)

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Assumptions

Research question

Do smokers and non-smokers differ in terms of

their lung capacity ?

Checking assumptions

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