Respuesta :
Answer:
Null hypothesis: [tex]p \leq 0.3[/tex]
Alternative hypothesis: [tex]p>0.3[/tex]
Step-by-step explanation:
For this question we need to take in count that the the claim that they want to test is "if the proportion is greater than 0.3". Our parameter of interest for this case is [tex]p[/tex] and the estimator for this parameter is given by this statistic [tex]\hat p[/tex] obtained from the info of sa sample obtained.
The sample proportion would be given by:
[tex] \hat p = \frac{X}{n}[/tex]
Where X represent the success and n the sample size selected
The alternative hypothesis on this case would be specified by the claim and the complement would be the null hypothesis. Based on this the system of hypothesis for this case are:
Null hypothesis: [tex]p \leq 0.3[/tex]
Alternative hypothesis: [tex]p>0.3[/tex]
And in order to check the hypothesis we can use the one sample z test for a proportion with the following statistic:
[tex] z = \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
The null hypotheses (H₀) should be less than or equal to 0.3 and the alternative hypotheses (Hₐ) should be greater than 0.3.
What are null hypotheses and alternative hypotheses?
In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
Testing to see if there is evidence that a proportion is greater than 0.3.
Our parameter of interest for the case is p and the estimate for this parameter is given by the statistics [tex]\rm \hat{p}[/tex] obtained from the info of sample obtained.
The sample proportion would be given by;
[tex]\rm \hat{p} = \dfrac{X}{n}[/tex]
where X be the success and n be the sample size selected.
The alternative hypothesis, in this case, would be specified by the claim and the complement would be the null hypothesis. Based on this the system of hypotheses for this case is;
Null hypotheses: p ≤0.3
Alternative hypotheses: p > 0.3
And in order to check the hypothesis, we can use the one-sample z test for a proportion with the following statistic.
[tex]\rm z = \dfrac{\hat{p} - p}{\sqrt \dfrac{p(1-p)}{n}}[/tex]
More about the null and alternative hypotheses link is given below.
https://brainly.com/question/16203205
