Sampling Distribution and Hypothesis testing
Hypothesis testing
1. Starting point: Null hypothesis: tails = 50%
2. Alternative hypothesis: Tails ≠ 50%
3. Probability 6 times tails: 1/64 = 1.6%
4. Conclusion: 1.6% < 5%
Reject null hypothesis & accept alternative hypothesis
Central question of the course: How is it possible to use one sample to draw a conclusion
about the population?
- Make a confirmation based on a sample about a population
Example; Chips
Previous research: µ regular = 80 grams
Research question: Is the mean consumption of light chips (in grams) higher than the mean
consumption of regular chips (in grams)?
Hypotheses
Null hypothesis: People eating light chips eat on average as much as people
eating regular chips → H0: µlight = 80
Alternative hypothesis: People eating light chips eat on average more than people eating
regular chips → H1: µlight > 80
Previous research: µregular = 80
50 people: light chips
Sample results: 𝑥 = 87
Problem: other sample → other result
How can we use the idea of a sampling distribution to draw a conclusion about the
population based on one sample?
P-value:
A small p-value (typically ≤ 0.05) indicates strong evidence against the null
hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to
reject the null hypothesis.
Sampling distribution for the mean:
1. We expect variation between samples
a. Sampling error: Natural discrepancy (chance fluctuation) between sample
statistic and corresponding population parameter
2. Most means will be around 80
Conclusion hypothesis test:
- Provides the sample result sufficient evidence against H0 (same chips
consumption)?
- Yes, if H0 is true, a mean of 87 is very unlikely
- Reject H0 & accept H1
- We have sufficient evidence that people eating light chips eat more than
people eating regular chips
Hypothesis Testing step by step
Hypothesis testing
1. Starting point: Null hypothesis: tails = 50%
2. Alternative hypothesis: Tails ≠ 50%
3. Probability 6 times tails: 1/64 = 1.6%
4. Conclusion: 1.6% < 5%
Reject null hypothesis & accept alternative hypothesis
Central question of the course: How is it possible to use one sample to draw a conclusion
about the population?
- Make a confirmation based on a sample about a population
Example; Chips
Previous research: µ regular = 80 grams
Research question: Is the mean consumption of light chips (in grams) higher than the mean
consumption of regular chips (in grams)?
Hypotheses
Null hypothesis: People eating light chips eat on average as much as people
eating regular chips → H0: µlight = 80
Alternative hypothesis: People eating light chips eat on average more than people eating
regular chips → H1: µlight > 80
Previous research: µregular = 80
50 people: light chips
Sample results: 𝑥 = 87
Problem: other sample → other result
How can we use the idea of a sampling distribution to draw a conclusion about the
population based on one sample?
P-value:
A small p-value (typically ≤ 0.05) indicates strong evidence against the null
hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to
reject the null hypothesis.
Sampling distribution for the mean:
1. We expect variation between samples
a. Sampling error: Natural discrepancy (chance fluctuation) between sample
statistic and corresponding population parameter
2. Most means will be around 80
Conclusion hypothesis test:
- Provides the sample result sufficient evidence against H0 (same chips
consumption)?
- Yes, if H0 is true, a mean of 87 is very unlikely
- Reject H0 & accept H1
- We have sufficient evidence that people eating light chips eat more than
people eating regular chips
Hypothesis Testing step by step
