**Hours Studied and Test Grades**The following table shows the hours studied and corresponding test grade earned by students on a recent test. Calculate the correlation coefficient, $r$, and determine whether $r$ is statistically significant at the 0.01 level of significance. Round your answer to the nearest thousandth.**Critical Values of the Pearson Correlation Coefficient**| Hours Studied and Test Grades ||-------------------------------|| **Hours Studied** | 0 | 0.5 | 1 | 1 | 2 | 2.25 | 3.25 | 3.5 | 3.75 | 3.75 | 4 | 5 || **Test Grade** | 72 | 64 | 68 | 81 | 79 | 85 | 82 | 72 | 99 | 87 | 84 | 97 | ### Statistical Significance of Pearson's Correlation Coefficient#### Determine the Significance of \[ r \]\[ r = \_\_\_\_\_\_\_\_\_ \]Is \[ r \] statistically significant at the 0.01 level of significance?**Instructions:**1. **Enter the value of \[ r \]**: Input the calculated Pearson's correlation coefficient value in the provided space.2. **Evaluate Significance**: Use statistical tables or software to determine if the value of \[ r \] is significant at the 0.01 level. The significance indicates how likely it is that the observed correlation is due to chance.**Step-by-Step Guide:**1. **Compute the Pearson's correlation coefficient (\[ r \])** using appropriate data.2. **Refer to the critical value table**: For a given degree of freedom \[ n-2 \], where \[ n \] is the sample size, find the critical value corresponding to the 0.01 significance level.3. **Compare \[ r \] value**: Check if the absolute value of \[ r \] is greater than the critical value from the table. If it is, then \[ r \] is statistically significant at the 0.01 level.**Concept Explanation:**- **Pearson's correlation coefficient (\[ r \])** measures the strength and direction of the linear relationship between two variables.- **Statistical significance** at the 0.01 level means there is only a 1% chance that the observed correlation occurred randomly, implying a 99% confidence level.**Further Reading:**- [Pearson Correlation Coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)- [Significance Testing](https://en.wikipedia.org/wiki/Statistical_significance)---This content helps you understand how to determine the statistical significance of a correlation coefficient in your data analysis, ensuring accurate and reliable results.

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Answered: The following table shows the hours…

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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The output below shows the relationship between stress and job performance: Correlation Stress Job performance Stress Pearson Correlation 1 Sig. (2-tailed) N 213 Job performance Pearson Correlation -.682** 1 Sig. (2-tailed) .000 N 213 213 **. Correlation is significant at the 0.01 level (2-tailed). Question: The correlation output shows what type of relationship?
What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below. Time Pounds 41 32 90 32 31 33 82 131 112 144 104 113 120 142 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?0 The p-value is: Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. O There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. O There is statistically significant evidence to…
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The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Hours Spent Studying 0 0.5 1.5 2 2.5 3 3.5 4 4.5 5.5 Midterm Grades 63 66 69 75 78 81 84 87 90 96 Estimate the correlation in words, positive, negative, no correlation. (a) Positive (b) Negative (c) No correlation
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nalysis Name: Date: Score: Section Exercise 10.3 1. SJS Company has been selling to retail customers in the Metro Manila area. They advertise extensively on radio, print ads, and in the internet. The owner would like to review the relationship between the amount spent on advertising expense (in P000s) and sales (in P000s). Below is information on advertising expense and sales for the last 9 months. Month Jan Advertising Expense 10 Sales Revenue Feb Mar Apr May June July Aug Sept 8 12 11 13 190 215 190 210 235 208 15 14 13 16 170 175 250 Find the coefficient of correlation. Determine at the 0.10 significance level whether the correlation in the population is greater than zero. Step 1: State the hypotheses. Ho: Hi: Step 2: The level of significance and critical region. a= Step 3: Complete the table and compute for the value of r and t. and tcritical = Month x x 22 x2 xy Jan Feb Mar Apr May Jun Jul Aug Sept Σχ= Σy= ΣΥ Σαν = Σx=- tcomputed= r = Step 4: Decision rule. Step 5: Conclusion.…
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(e)
Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 31.80 52.94 85.82 102.16 60.17 111.77 D 5.46 6.07 15.82 15.40 11.15 20.32 Construct a scatterplot. Choose the correct graph below. O A. O B. Oc. D. Q 25- 25- 25 0- 30 0- 30 Bill Amount ($) 0+ 30 Bill Amount (S) 0- 30 Bill Amount (S) 120 120 120 Bill Amount (S) 120 The linear correlation coefficient is r= 0.954 (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: p H,: P (Type integers or decimals. Do not round.) Tip Amount ($) ip Amount ($) Tip Amount ($) Tip Amount ($)

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