Answer these questions The image displays a statistical analysis task related to earnings per share and dividends per share for six companies in a recent year. The focus is on determining the type of correlation, if any, between these two variables using data and a correlation coefficient.### Data Table:- **Earnings per Share (x):** 1.55, 4.05, 1.99, 1.15, 0.39- **Dividends per Share (y):** 0.83, 0.47, 2.34, 1.11, 0.71, 1.46### Correlation Analysis:- A section labeled (c) asks to describe the type of correlation. The user has noted "no linear correlation."- The instructions are to interpret the correlation by choosing the correct statement: - Options explore relationships like increased earnings leading to increased dividends, a lack of observed relationships, and whether there is an apparent linear correlation. - Option E, chosen by the user, states: "Based on the correlation, there does not appear to be a linear relationship."### Critical Value:- Section (d) asks for the use of critical values for the Pearson correlation coefficient to determine significance at the 1% level.- The critical value is left blank, and there's a space to conclude about the relationship between earnings per share and dividends per share.The page includes features like "Help me solve this," "View an example," and "Get more help," indicating it is an educational resource that aids in understanding statistical concepts related to correlation in financial data. The image displays a statistical analysis exercise involving the correlation between earnings per share and dividends per share for six companies. Here's a detailed transcription:**Educational Task: Understanding Correlation**The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for six companies in a recent year. Complete parts (a) through (d) below.---Round to three decimal places as needed.**(c) Describe the type of correlation, if any, and interpret the correlation in the context of the data.**There is [__no__] linear correlation.*Interpret the correlation. Choose the correct answer below:*A. Increases in companies' earnings per share cause their dividends per share to increase.B. As companies' earnings per share increase, their dividends per share tend to increase.C. As companies' earnings per share increase, their dividends per share tend to decrease.D. Based on the correlation, there does not appear to be any relationship between companies' earnings per share and their dividends per share.E. Based on the correlation, there does not appear to be a linear relationship between companies' earnings per share and their dividends per share.F. Increases in companies' earnings per share cause their dividends per share to decrease.**Correct answer: E.** Based on the correlation, there does not appear to be a linear relationship between companies' earnings per share and their dividends per share.**(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation at the 1% level of significance.**The critical value is [__]. Therefore, there [__is not__] sufficient evidence at the 1% level of significance to conclude that there is a significant linear correlation between companies' earnings per share and their dividends per share.(Round to three decimal places as needed.)---**Additional Features:**Buttons included for user support:- Help me solve this- View an example- Get more helpThis analysis helps users understand how to interpret correlation data and recognize when a linear relationship exists in financial metrics.

State the null hypotheses.Use EXCEL to obtain the value correlation coefficient r: EXCEL procedure: Go to EXCEL Go to Data>Data Analysis. Choose Correlation. Enter the range as $A$1:$B$7. Check the option Labels in First row. Click OK. EXCEL output: From the EXCEL output, the value of the correlation coefficient is 0.0868 Thus, the value of correlation coefficient is 0.0868 From the information, given that n=6 and r=0.0868 From the” critical value of r table”, the critical value of r at the 0.01 significance level at the sample of size 6 is 0.917 Thus, the critical value of r is 0.917. The conclusion is obtained as shown below: Conclusion: Use the level of significance is 0.01. The critical value of r is 0.917 and the calculated value is 0.0868 By rejection rule, reject the null hypothesis. That is, there is sufficient evidence to conclude that there is s linear correlation between companies earnings per share and their dividends per share. Thus, the critical value is 0.917. There is sufficient evidence at 1% level of significance to conclude that there is a significant linear correlation between companies earnings per share and their dividends per share.

The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for 6 companies in a recent year. Complete parts (a) through (d) below. Click here to view the data table. Click here to view the table of critical values for the Pearson correlation coefficient, D ..... (Round to three decimal places as needed.) - X (c) Describe the type of correlation, if any, and interpret the correlation in th Data table There is no linear correlation. Earnings per share, x 1.55 Dividends per share, y o 0.83 0.47 2.34 Interpret the correlation. Choose the correct answer below. 4.41 3.79 8.9 1.95 3.39 OA. Increases in companies' earnings per share cause their dividends p 1.11 O B. As companies' eamings per share increase, their dividends per sha O C. As companies' earnings per share increase, their dividends per sha 0.71 1.46 O D. Based on the correlation, there does not appear to be any relations VE. Based on the correlation, there does not appear to be a linear relati Print Done OE Increases in companies' earnings per share cause their dividends p (d) Use the table of critical values for the Pearson correlation coefficient to V between companies' earnings per share and their dividends pe V sufficient evidence at the 1% level of significance to conclude that The critical value is Therefore, there share. (Round to three decimal places as needed.) Check an Clear all 7:40A Get more help - View an example 11/16/2 Help me solve this 62°F Partly sunny 日, P Type here to search

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...

See similar textbooks