P-Values and Hypothesis Testing Concepts

What is the primary goal of statistical inference?

• To summarize and describe existing datasets.

• To make educated guesses about data that has not yet been collected.

• To create visual representations of data.

• To calculate exact population parameters.

If a sample of students listening to Mozart scored 3 points higher on average than a sample of students working in silence, why is this not sufficient to conclude that listening to Mozart improves calculus grades for the entire student population?

• The sample size was too small to be representative.

• Sample parameters are only estimates of the true population parameters.

• The students were not randomly assigned to groups.

• The difference of 3 points is not statistically significant.

You and a friend have different hypotheses about the average number of spots on baby giraffes. After collecting a sample of 25 baby giraffes with a mean of 200 spots, you compare it to your model (average 175 spots) and your friend's model (average 209 spots). If your model shows 200 spots as a rare outcome (top 1.2% values) and your friend's model shows 200 spots as a more common outcome (top 32% values), whose model is better supported by the data?

• Your model, because 200 is closer to 175 than 209.

• Your friend's model, because 200 is a more likely outcome under their hypothesis.

• Neither model, as the sample mean is exactly between the two hypothesized means.

• Both models are equally supported, as they both predict a normal distribution.

Null Hypothesis Significance Testing (NHST) is described as a form of reductio ad absurdum. What does this mean in the context of hypothesis testing?

• It directly proves a hypothesis by showing its truth.

• It discredits an idea by assuming it's true and demonstrating a contradictory outcome.

• It involves reducing complex hypotheses to simpler, more absurd statements.

• It aims to find the most absurd possible explanation for observed data.

What does a P-value represent in statistical analysis?

• The likelihood that the alternative hypothesis is true.

• The probability of observing data as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.

• The chance of making a Type I error.

• The strength of the relationship between two variables.

If a one-sided P-value for a sample mean being higher than 2400 is 8.99%, and the distribution of sample means is symmetrical around a population mean of 2300, what would be the two-sided P-value for a sample mean as extreme as 2400?

• 8.99%

• 4.495%

• 17.98%

• 91.01%

If the null hypothesis states there is no effect of Gene X on caloric intake, and a study yields a two-sided P-value of 0.18, what does this P-value indicate?

• There is an 18% chance that Gene X has a significant effect on caloric intake.

• There is an 18% chance of observing a sample mean as extreme as the one found, purely due to random variation, if Gene X has no effect.

• The study has an 18% probability of making a Type II error.

• The effect of Gene X is 18% stronger than expected.

In null hypothesis significance testing, what does a P-value cutoff of 0.05 typically signify?

• The sample value must be exactly 5% different from the population mean.

• The probability of the null hypothesis being true is 5%.

• The sample value must be in the top 5% of the most extreme values in the distribution to be considered evidence against the null hypothesis.

• There is a 5% chance of the alternative hypothesis being true.