### Understanding the Difference in Pass Rates: Morning vs. Afternoon SectionsA university department chair believes that the afternoon section of a large survey class has a consistently lower proportion of students that pass the class compared to the morning section. To investigate this hypothesis, the chair checks a random sample of student records from each section. The results of the data collected are shown below.#### Data Summary:**Morning Section:**- Successes: 346- Observations: 400- Sample Proportion (\( \hat{p}_1 \)): 0.865**Afternoon Section:**- Successes: 426- Observations: 500- Sample Proportion (\( \hat{p}_2 \)): 0.852**Statistical Analysis:**- Confidence Level: 95%- \( z \)-score: -0.5548- \( p \)-value: 0.2912#### Interpretation of Results:The \( z \)-score and \( p \)-value indicate the statistical significance of the difference between the passing rates of the two sections. Given the \( p \)-value of 0.2912, which is higher than the common significance level of 0.05, we do not have sufficient evidence to reject the null hypothesis. This means there is no significant difference in the passing rates between the morning and afternoon sections at the 95% confidence level.#### Diagram Explanation:The provided figure is a normal distribution curve. The shaded area under the curve represents the region associated with the \( p \)-value. The curve extends from -3 to +3 standard deviations, with a marked \( z \)-score of -0.5548. Here, the \( z \)-score corresponds to the position on the curve relative to the mean, while the shaded area visually denotes the \( p \)-value region, showcasing that the result is not statistically significant.#### Calculation Details:To strengthen your understanding, you may manually input values and verify calculations:1. Morning section samples (\( n_1 \)): Example: 92. Afternoon section samples (\( n_2 \)): (Input specific values)3. Sample proportion for morning section (\( \hat{p}_1 \)): Example: 1.2344. Sample proportion for afternoon section (\( \hat{p}_2 \)): (Input specific values)By examining the data and statistical exhibits, we validate

Let n1 be the number of observations in the morning section. x1 be the number of successes in the…

A university department chair believes that the afternoon section of a large survey class has a consistently lower proportion of students that pass the class compared to the morning section. The chair checks a random sample of student records from each section. The results of the data collected are shown below. Morning section Afternoon section Successes 346 Successes 426 500 Observations 400 Observations p-hat_1 0.865 p-hat 2 0.852 Confidence level 95% z-score -0.5548 p-value 0.2912 -3 2 3 P = Ex: 1.234 Z= Morning section samples: n₁ = Ex: 9 Afternoon section samples: n₂ = Sample proportion for morning section samples: p₁ = Ex: 1.234 Sample proportion for afternoon section samples: P₂ =