Here are the statements with their explanations:

Statement Analysis:

1. The p-value depends on the data.
   True.
   The p-value is calculated from the data collected during an experiment. It represents the probability of observing a test statistic as extreme as, or more extreme than, the one observed under the assumption that the null hypothesis is true.

2. If the p-value is smaller than 5%, then there is less than a 5% chance that the null hypothesis is true.
   False.
   The p-value does not provide the probability that the null hypothesis is true. Instead, it gives the probability of observing the data (or something more extreme) assuming the null hypothesis is true.

3. If the null hypothesis is true, then there is less than a 5% chance to get a p-value that is smaller than 5%.
   True.
   If the null hypothesis is true, the p-value follows a uniform distribution, meaning that the chance of obtaining a p-value less than 5% (if the significance level is 5%) is exactly 5%.

4. If a data scientist does many tests, then even if all the null hypotheses are true, a certain proportion will be rejected in error.
   True.
   This describes the multiple testing problem. When many hypothesis tests are conducted, the likelihood of falsely rejecting at least one true null hypothesis (Type I error) increases. For example, with a significance level of 5%, 5% of the tests are expected to yield significant results by chance.

Correct Answers:

1. The p-value depends on the data.
2. If the null hypothesis is true, then there is less than a 5% chance to get a p-value that is smaller than 5%.
3. If a data scientist does many tests, then even if all the null hypotheses are true, a certain proportion will be rejected in error.

Do you want a deeper explanation for any of these?

Related Questions:

1. What does a p-value actually measure in hypothesis testing?
2. Why is it incorrect to interpret a p-value as the probability of the null hypothesis being true?
3. How does the concept of Type I error relate to p-values and significance levels?
4. What are some techniques to correct for multiple hypothesis testing?
5. How does the uniform distribution of p-values work under the null hypothesis?

Tip:

Always complement hypothesis testing with confidence intervals to better understand the results!