Nathan VanHoudnos

11/3/2014

- Homework comments
- Checkpoint comments
- Lecture 18 (covers pp. 192-198)

**FALSE**: The 95% confidence interval I just calculated has a 95% chance of containing the true value.**FALSE****TRUE**: Over many repeated experiments, 95% of the confidence intervals you construct will contain the true value.**TRUE**

- Point estimation
- Interval estimation
- Confidence Intervals – If we repeat the experiment over and over, 95% of intervals will contain the true value.
- Credible Intervals – If we do the experiment once, the probability that the true value is contained within the interval is 95%.

- Confidence Intervals – If we repeat the experiment over and over, 95% of intervals will contain the true value.
**Hypothesis Testing**- can be useful
- and, yet, as it stands, is a literal pox upon science.

A case of suspected cheating on an exam is brought in front of the disciplinary committee at a certain university.

There are two opposing claims in this case:

The student's claim: I did not cheat on the exam.

The instructor's claim: The student did cheat on the exam.

“innocent until proven guilty”

- the instructor must give
**sufficient evidence**that the**claim of innocence**is unlikely

The instructor says:

- The exam had two versions with different values of \( \mu \), \( \sigma \), and \( n \) between the two versions.
- This student used the values of \( \mu \), \( \sigma \), and \( n \) from the
**other exam version**to get the answer. - The student did this for
**three**out of the four exam questions.

“innocent until proven guilty”

- the instructor must give
**sufficient evidence**that the**claim of innocence**is unlikely

The instructor says the student used the other set of numbers for three out of the four exam questions.

Is this sufficient evidence to **reject the claim of innocence** ?

Yes. We can reject the claim of innocence.

**Step 1**: State the claims.
\[ \begin{aligned}
H_0 & \text{ : null hypothesis} &
H_A & \text{ : alt. hypothesis}
\end{aligned} \]

- \( H_0 \) the student is innocent
- \( H_A \) the student is guilty

**Step 2**: Present evidence against \( H_0 \)

- The instructor presents evidence that the student cheated.

**Step 3**: Decide if \( H_0 \) should be rejected or retained.

- \( H_0 \) is rejected. The student cheated.

**Karl Popper**

1902 - 1994

Claim:

All swans are white.

Finding millions upon millions of white swans does not prove this claim.

If, there exists a single black swan, then the claim is false.

Popper argued that, if a theory is **falsifiable**, then it is scientific.

**Louis de Broglie**

1892 - 1987

Before quantum mechanics, scientists thought that electrons, protons, neutrons and the like were essentially little billiard balls.

- \( H_0 \) (prevailing model) The electron is a particle.
- de Broglie's (1924) Ph.D. thesis showed that electrons act like waves.
- \( H_0 \) is rejected, and quantum mechanics gains strength

**Karl Pearson**
1857-1936