Respuesta :
Answer:
Answered
Step-by-step explanation:
let you have an interest in establishing the success of the method be p
as higher the p value ; higher the evidence of method success
hence the p value of 0.001 is preferred because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective,
Answer:
Null hypothesis:[tex]p \leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
For this case we assume that the calculated value its [tex] z_{calc}[/tex]
And the p value for this case would be given by:
[tex] p_v = P(Z>z_{calc}[/tex]
And for this case we want that the [tex]p_v < \alpha[/tex] in order to reject the null hypothesis and on that case we will have enough evidence to conclude that the true proportion of having a girl with the method is >0.5 and that's our interest, so then we need the lowest p value in order to have more evidence to reject the null hypothesisand conclude that the method is effective. The answer for this case would be 0.001.
Step-by-step explanation
Data given and notation
n represent the random sample taken
[tex]\hat p[/tex] estimated proportion of interest
[tex]p_o=0.7[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion of having a girl is higher than 0.5, the system of hypothesis on this case are.:
Null hypothesis:[tex]p \leq 0.5[/tex]
Alternative hypothesis:[tex]p > 0.5[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
For this case we assume that the calculated value its [tex] z_{calc}[/tex]
And the p value for this case would be given by:
[tex] p_v = P(Z>z_{calc}[/tex]
And for this case we want that the [tex]p_v < \alpha[/tex] in order to reject the null hypothesis and on that case we will have enough evidence to conclude that the true proportion of having a girl with the method is >0.5 and that's our interest, so then we need the lowest p value in order to have more evidence to reject the null hypothesisand conclude that the method is effective. The answer for this case would be 0.001.
