Hypothesis Testing for b₀ using the formula

               Null Hypothesis:               H_o: b₀ = 0      (i.e. y-intercept is not significant)

               Alternative Hypothesis:     H_a: b₀  0    (i.e. the y-intercept is significantly different from zero)

You will use the test statistic, t*,  that you found in the "using the formula" section of this lesson to determine whether or not to reject the null hypothesis.

test statistics = t* = -6.02  (To review how to find this value click here.)

• If |t*| > t_critical, then reject the null and accept the alternative.  
• If |t*| < t _critical, then there is not enough evidence to reject the null (i.e. Do not reject the null.)

For a 5% significance level (which is the same as a 95% confidence level) and 5 degrees of freedom: t _critical = 2.571   (This value is found from a t-table.)

Since   |-6.02|>2.571   (|t*| > t_critical),  we reject the null and accept the alternative which is b₀ not =0.  

This tells us that the y-intercept is significantly different from zero.  When we model the amount of water consumed based on temperature, we will include the y-intercept in the model. 
More information can be gathered by computing the 95% confidence coefficient for b₀.

 95% Confidence interval for b₀     = b₀ + t _critical*s(b₀)
                                                                      = -96.85 + 2.571(16.15)
                                                        = (-138.37, -55.33) 

Interpretation of the Confidence Interval

We are 95% confident that when the temperature is 0 degrees Fahrenheit,  between -138.37 and -55.33  ounces of water are consumed. 

 Remember to review the terms for hypothesis testing and confidence intervals for b₀

Learn the Procedure for testing the hypotheses and constructing confidence intervals

Y-Intercept Inference Menu    Dictionary

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