Are the following statements $\mathrm { H } _ { 0 } : \mu \geq 6 \mathrm { H } _ { \mathrm { A } } : \mu \leq 19$ a valid pair of null and alternative hypotheses?
A) No, there are no parameters contained in these statements
B) No, the alternative hypothesis cannot contain numeric values
C) No, these statements have overlapping regions
D) No, these statements both compare a parameter to a value

Question

Quizplus · Accepted Answer

These statements have overlapping regions because if $\mu$ falls between 6 and 19, it satisfies both the null and alternative hypothesis, making the hypotheses contradictory. The null and alternative hypotheses should be mutually exclusive (i.e. $\mu$ is either greater than or equal to 6, or less than or equal to 19).

Are the Following Statements H0:μ≥6HA:μ≤19\mathrm { H } _ { 0 } : \mu \geq 6 \mathrm { H } _ { \mathrm { A } } : \mu \leq 19H0​:μ≥6HA​:μ≤19

Are the Following Statements $\mathrm { H } _ { 0 } : \mu \geq 6 \mathrm { H } _ { \mathrm { A } } : \mu \leq 19$