## Math Problem Statement

A random sample of 115 married or de facto couples in the Sydney region has been selected to study non-verbal communication. An experiment was conducted requiring the subject to guess words shown to the partner, without any verbal communication. Some of the variables recorded for each couple are listed below.

**VariableDescription**

subid

Subject ID

sex

sex of guesser

years

the length of the relationship (in years)

percentage

the percentage of correct guesses

A simple linear regression is run to answer the research question, ’What is the relation between the percentage of correct guesses and the length of the relationship (in years)?’ The results of the analysis are reported below:

```
Estimate Std. Error t value Pr(>|t|)
```

(Intercept) 37.4612 2.7930 13.4123 0
`years 0.7307 0.0687 10.6365 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. There is no relation whatsoever, linear or non-linear, between the two variables

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

e. The relation between the two variables is linear

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

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 10.64 times the population standard deviation1.96 times the population standard deviation1.96 times its standard error10.64 times its standard error

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?

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Linear Regression

Hypothesis Testing

Statistics

### Formulas

t = Estimate of the slope / Standard Error of the slope

Simple Linear Regression formula: y = b0 + b1*x

### Theorems

t-distribution

Hypothesis Testing for Regression Slope

### Suitable Grade Level

Undergraduate Statistics

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