Respuesta :
Answer:
There is sufficient evidence to reject the claim [tex]\mu[/tex] < 104
Step-by-step explanation:
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
2) Solution to the problem
On this case we want to test is [tex]\mu<104[/tex]
So the correct system of hypothesis for this case would be:
Null hypothesis: [tex]\mu \geq 400[/tex]
Alternative hypothesis: [tex] \mu < 400[/tex]
how should you interpret a decision that fails to reject the null hypothesis?
There is not sufficient evidence to reject the claim [tex]\mu[/tex] < 104.
False, we fail to reject the null hypothesis so then the alternative is rejected, and the alternative hypothesis represent the claim
There is sufficient evidence to reject the claim [tex]\mu[/tex] < 104
True, since the claim it's the alternative we need to establish the conclusion in terms on the claim, and on this case makes sense, since we don't have enough info to support the alternative hypothesis since we fail to reject the null hypothesis.
There is sufficient evidence to support the claim [tex]\mu[/tex] < 104.
False, we FAIL to reject the null hypothesis that the mean it's greater or equal than 104 so not makes sens say that we support the alternative hypothesis.
There is not sufficient evidence to support the claim [tex]\mu[/tex] < 104
False, the statement is not incorrect but the proble it's that we are not rejecting the alternative hypothesis, we FAIL to reject the null so that's not the appropiate way to describe the result
