Question

PROBLEM #2: (Multiple Choice) Choose the correct answer. Suppose the systolic blood pressure is roughly a linear function of the urinary sodium content and the slope is β₁. For the test H₀: vs. β₁ = 0   vs   H_a: vs. β₁ > 0

you reject the H₀. Which of the following statements

is true.

⑴ You can not make a Type I error.

⑵ You can not make a right decision.

⑶ You can not make a Type II error.

⑷ None of the above.

Answer 1

Answer: ⑴ You can not make a Type I error.

The null and alternative hypotheses for a hypotheses test about the slope are :

H₀ : β₁ = 0
H_a : β₁ > 0.

This can be used to test whether or not systolic blood pressure and urinary sodium content are linearly related. The slope β₁, directly tells us about the link between the mean systolic blood pressure and urinary sodium content. When the true population slope does not equal 0, the variables systolic blood pressure and urinary sodium content are linearly related. When the slope is 0, there is not a linear relationship because the mean systolic blood pressure does not change when the value of urinary sodium content is changed.

As it is given that the systolic blood pressure is roughly a linear function of the urinary sodium content with slope is β₁ , by rejecting null hypothesis we are making a correct decision. So there are no chance of making type I error, as type I error is only made when null hypothesis is true and we are rejecting it.