**Exploring the Relationship Between Study Time and Exam Scores**In a survey conducted to study the relationship between the amount of time statistics students spend studying per week and their final exam scores, the following data was collected:| Time (hours) | 11 | 5 | 7 | 1 | 2 | 1 | 7 | 4 ||--------------|----|---|---|---|---|---|---|---|| Score | 82 | 68| 70| 63| 62| 54| 78| 69|To analyze the data, we need to consider the following steps:- **x-values** represent the time students spent studying each week.- **y-values** represent the scores obtained by these students in their final exams.**a. Correlation Coefficient:**Determine the correlation coefficient, \( r \), which measures the strength and direction of the linear relationship between the two variables. Calculate \( r \) and round the answer to 2 decimal places.**b. Hypotheses for Correlation:**Set up the null and alternative hypotheses for testing the correlation:- \( H_0: \rho = 0 \) (No correlation between study time and scores)- \( H_1: \rho \neq 0 \) (There is a correlation)**c. P-value:**Calculate the p-value, which indicates the probability of observing the data if the null hypothesis is true. Record the p-value, rounded to four decimal places. This analysis will help determine if there is a statistically significant relationship between the time spent studying and the exam scores among the surveyed students.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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