Respuesta :
Answer:
If we define the random variable X ="time spend by the students doign homework"
And we want to tes t is students spend more than 1 hour doing homework per night, on average (alternative hypothesis), so then the system of hypothesis for this case are:
Null hypothesis: [tex] \mu \leq 1[/tex]
Alternative hypothesis: [tex]\mu >1 [/tex]
And they wnat to use a sample size of n = 100 and a significance level of 0.05
Step-by-step explanation:
Previous concepts
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".
Solution to the problem
If we define the random variable X ="time spend by the students doign homework"
And we want to tes t is students spend more than 1 hour doing homework per night, on average (alternative hypothesis), so then the system of hypothesis for this case are:
Null hypothesis: [tex] \mu \leq 1[/tex]
Alternative hypothesis: [tex]\mu >1 [/tex]
And they wnat to use a sample size of n = 100 and a significance level of 0.05
You can choose the correct null hypothesis. We test if the null hypothesis is wrong.
We test the incorrectness of the hypothesis which assumes that the students only spend usually 1 hour doing homework per night.
Thus, principal will test the null hypothesis Null hypothesis = [tex]H_0: \mu = 1 \: \rm hour[/tex] and would like to know if it is wrong or not.
How to form the hypotheses?
There are two hypothesis. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
For the current case, since the principal wants to know if students spend more than 1 hour doing homework per night, we will assume(hypothesize) that students do just 1 hour study per night usually.
Thus, Null hypothesis = [tex]H_0: \mu = 1 \: \rm hour[/tex]
(and thus, principle wants to disprove this hypothesis as he/she wants to know if students spend more than 1 hour per night generally.)
Alternate hypothesis will be that the students do more than 1 hour study per night averagely.
Thus, Alternate hypothesis = [tex]H_1: \mu > 1 \: \rm hour[/tex] (one tailed test since its on one side of 1(bigger side))
Thus, principal will test the null hypothesis Null hypothesis = [tex]H_0: \mu = 1 \: \rm hour[/tex] and would like to know if it is wrong or not.
Learn more about null and alternate hypothesis here:
https://brainly.com/question/18831983
