## Problem Set 1: Spatial Memory and Chemotherapy

### Problem Description:

A researcher investigates the impact of chemotherapy on spatial memory in rats. The experiment involves training 25 rats in a maze for 30 days, and data on completion times during the last 5 days are collected.

**Graphical Representation:
**

**Graph 1: estimated marginal means vs. factor for chemotherapy on rats**

**Statistical Hypothesis:
**

**Null Hypothesis:**The mean completion times for rats are the same over the last five days of training.**Alternative Hypothesis:**The mean completion times for rats differ for at least two of the last five days.**Statistical Test:**Repeated measures ANOVA (no follow-up comparison needed).

**Descriptive Statistics:
**

- Estimates for the Last 5 Days:

**Statistical Hypothesis Test Result:
**

- Tests of Within-Subjects Effects

**Verbal Description of Scientific Result:
**

- Since p-value (0.621) > 0.05, we fail to reject the null hypothesis. No significant difference, so the second phase of the experiment is not warranted.

## Problem Set 2:

**Nausea Medications
**

**Problem Description:** The study compares the effectiveness of three nausea medications.

**Graphical Representation:
**

**Graph 2: estimated marginal means vs. drug for nausea medication**

**Statistical Hypothesis:
**

**Null Hypothesis:**The three nausea medications have the same mean severity of symptoms.**Alternative Hypothesis:**At least two of the three nausea medications have different mean severity of symptoms.**Statistical Test:**ANOVA with post hoc LSD tests.

**Statistical Test Result:**

- ANOVA
- Multiple Comparisons (LSD)

**Result Description:
**

- Since p-value (0.000) < 0.05, reject the null hypothesis. All three drugs have significantly different means of symptom severity.

## Problem Set 3: Seizure Reduction Drug

### Problem Description:

Researchers test a new drug's effectiveness in reducing seizures.

**Expected Effect Size (Cohen's d):
**

**Cohen's d:**0.9607689 (95% CI: -0.5572812 to 2.411237)

**Sample Size Calculation:
**

**Control group:**23, Treated group: 23 (to detect a significant effect).

**Pre/Post Design Sample Size:
**

**Total sample size:**12 (assuming effect size remains the same).

**New Drug Evaluation:
**

- Use power analysis to determine the trade-offs between increased effectiveness (20%) and higher cost (50%).

## Problem Set 4: Chicken Pox Severity

### Problem Description:

The study explores how the age of onset impacts the severity of chickenpox in children.

**Graphical Representation:
**

**Graph 3: estimating symptom severity depending on the participant’s age**

**Statistical Hypothesis:
**

**Null Hypothesis:**Age of onset has no impact on chicken pox severity.**Alternative Hypothesis:**Age of onset impacts chicken pox severity.

**Statistical Test Result:**

Regression Coefficients:

**Intercept:**6.8667 (p < 0.01)**ParticipantAge:**-0.2751 (p < 0.01)

**Predicted Severity at Age 5:
**

**Predicted:**5.491 (95% CI: 5.277 to 5.706)- Prediction is considered good.

**Prediction for 20s:
**

- No, as the model predicts negative severity, which is out of the range (0 - 10).

**Problem Set 5:** Blood Sugar Levels and Cereals

### Problem Description:

The study examines how different cereals affect short-term blood sugar levels.

**Graphical Representation:
**

**Graph 4: the effects of cereals on blood sugar levels**

**Censoring in Data:
**

- Right and Type I censoring.

**Statistical Test and Null Hypothesis**:

- Statistical Test: Log-rank test.
- Null Hypothesis: No difference in the probability of blood sugar dropping below 100 at any time point.

**Descriptive Statistics:
**

**Result Description:
**

**Chi-Square (Log Rank):**7.030 (df = 1, p = 0.008).- Reject the null hypothesis, indicating a significant difference between populations in the probability of blood sugar dropping below 100.