 Hypothesis Testing for b0 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:               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.)

• If |t*| > tcritical, 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*| > 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 for b0

(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

STATS @ MTSU

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