Hypothesis Testing for b0 using the formulaTo test for the significance of the y-intercept in the linear model, we first need to establish the null and alternative hypotheses:
Null Hypothesis: Ho: b0 = 0 (i.e. y-intercept is not significant)
Alternative Hypothesis: Ha: 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.)
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*| > tcritical), 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.
Construct a 95% Confidence Interval forb0
(1-a)100% Confidence Interval for b0 is b0 + t critical*s(b0), where
b0 = -96.85
s(b0) = 16.15 (To review computations click here.)
t critical = 2.571 (Found from a t-table.)
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
STATS @ MTSU