## Math Problem Statement

A random sample of 140 teams playing in major international team sporting competitions has been selected to study corporate sponsorship and subsequent sporting success. Some of the variables recorded for each team are listed below.

**VariableDescription**

subid

Subject ID

sex

sex of players

numSponsors

number of distinct corporate sponsors

percentWin

the percentage of international games won

A simple linear regression is run to answer the research question, ’What is the relation between the percentage of international games won and number of distinct corporate sponsors?’ The results of the analysis are reported below:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 38.2271 2.4433 15.6459 0
`numSponsors 0.7093 0.0649 10.9362 0`

Address the following questions, assuming as necessary that all test assumptions are verified.

What is the null hypothesis? Choose one among the following options:

a. The slope of the regression line is zero

b. There is a significant relation, linear or non-linear, between the two variables

c. The slope of the regression line is significantly different from zero

d. There is no relation whatsoever, linear or non-linear, between the two variables

e. The slope of the regression line is either positive or negative

f. The relation between the two variables is linear

Answer 1 Question 3 abcdef

From the test statistic as reported above, we can conclude that the estimated value of the slope is:

Answer 2 Question 3 10.94 times its standard error1.96 times its standard error1.96 times the population standard deviation10.94 times the population standard deviation

From the p-value as reported above, we can conclude that the decision of the test is:

Answer 3 Question 3 Accept H0Reject H0Do not accept H0Do not reject H0

What is the conclusion of the test?

Answer 4 Question 3 There is evidence of a linear relationship between these two variables.There is no evidence of a linear relationship between these two variables.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Statistics

Linear Regression

Hypothesis Testing

### Formulas

Simple Linear Regression: y = β0 + β1x

Test Statistic = β1 / SE(β1)

p-value calculation for hypothesis testing

### Theorems

Null Hypothesis for Regression

Slope Interpretation in Regression

p-value Significance Testing

### Suitable Grade Level

College level statistics or advanced high school (Grades 11-12)

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