Question

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical​ trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of pgreater than​0.5, which corresponds to the claim that the method increases the likelihood of having a​ girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the​ method, which of the following​ P-values would you​ prefer: 0.999,​ 0.5, 0.95,​ 0.05, 0.01,​ 0.001? Why?

Answer 1

Null hypothesis:
`p \leq 0.5`

Alternative hypothesis:
`p > 0.5`

When we conduct a proportion test we need to use the z statistic, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

For this case we assume that the calculated value its
`z_(calc)`

And the p value for this case would be given by:

`p_v = P(Z>z_(calc)`

And for this case we want that the
`p_v < \alpha` 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

`\hat p` estimated proportion of interest

`p_o=0.7` is the value that we want to test

`\alpha` represent the significance level

z would represent the statistic (variable of interest)

`p_v` 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:
`p \leq 0.5`

Alternative hypothesis:
`p > 0.5`

When we conduct a proportion test we need to use the z statistic, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

For this case we assume that the calculated value its
`z_(calc)`

And the p value for this case would be given by:

`p_v = P(Z>z_(calc)`

And for this case we want that the
`p_v < \alpha` 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.

Answer 2

Answered

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,