Aug 7, 2024

**Current Situation**: Website has an off-white background, average user time is 20 minutes.**Goal**: Increase user time by changing the background color to yellow.

**Null Hypothesis (H0)**: The mean user time remains 20 minutes after the change.**Alternative Hypothesis (H1)**: The mean user time is greater than 20 minutes after the change.

**Significance Level ((\alpha))**: Typically set at 1%, 5%, or 10%.**Chosen Level for Example**: 0.05 (5%).

**Sample Size (n)**: 100 users.**Sample Mean**: Calculate the mean time spent on the site by the sample.**Sample Standard Deviation**: Calculate if population standard deviation is unknown.

**P-value Definition**: Probability of obtaining a sample mean as extreme as the observed one, assuming the null hypothesis is true.**Conditional Probability**: ( P(\text{Sample Mean} \geq 25 \text{ minutes} | H0 \text{ is true}) ).**Tools**: Use t-statistic if the sampling distribution is roughly normal.

**If P-value < (\alpha)**: Reject the null hypothesis.**If P-value (\geq) (\alpha)**: Do not reject the null hypothesis.

**Observed Sample Mean**: 25 minutes.**P-value**: Calculated from the sample data.**Scenario 1**: P-value = 0.03- Since 0.03 < 0.05, reject the null hypothesis. Have evidence that the mean user time increased.

**Scenario 2**: P-value = 0.50- Since 0.50 > 0.05, cannot reject the null hypothesis. No evidence that the mean user time increased.

**P-value Interpretation**: Probability of getting the sample statistics given that the null hypothesis is true.**Common Confusion**: It is NOT the probability that the null hypothesis is true given the sample data.