Hypothesis Testing for b_{0} using the formula
To test for the significance of the y-intercept in the linear model, we first need to establish the null and alternative hypotheses:Null Hypothesis: H_{o}: b_{0} = 0 (i.e. y-intercept is not significant)
Alternative Hypothesis: H_{a}: b_{0} 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*| > t_{critical}), we reject the null and accept the alternative which is b_{0 }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 b_{0}.
Construct a 95% Confidence Interval for b_{0}
(1-a)100% Confidence Interval for b_{0} is b_{0} + t_{ critical}*s(b_{0}), where
b_{0} = -96.85
s(b_{0}) = 16.15 (To review computations click here.)
t_{ critical} = 2.571 (Found from a t-table.)
95% Confidence interval for b_{0}
= b_{0} + t_{ critical}*s(b_{0})
= -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 b_{0}
Learn the Procedure for testing the hypotheses and constructing confidence intervals
Y-Intercept Inference Menu Dictionary
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