Mathematics, 17.12.2019 02:31, clewis57

The genetics and ivf institute conducted a clinical trial of the ysort method designed to increase the probability of conceiving a boy. as this book was being written, 51 babies were born to parents using the ysort method, and 39 of them were boys. use the sample data with a 0.01 significance level to test the claim that with this method, the probability of a baby being a boy is greater than 0.5. does the method appear to work?

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answered: destinyaus14

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: p 0.5

$z=\frac{0.765 -0.5}{\sqrt{\frac{0.5(1-0.5)}{51}}}=3.785$

$p_v =P(z3.785)=7.68x10^{-5}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.01$ we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of boys is significantly higher than 0.5.

Step-by-step explanation:

1) Data given and notation

n=51 represent the random sample taken

X=39 represent the number of boys

$\hat p=\frac{39}{51}=0.765$ estimated proportion of boys

p_o=0.5 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that with this method, the probability of a baby being a boy is greater than 0.5.:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: p 0.5

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

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.765 -0.5}{\sqrt{\frac{0.5(1-0.5)}{51}}}=3.785$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z3.785)=7.68x10^{-5}$

answered: Guest

step-by-step explanation:

no of data

divide by no of mode

answered: Guest

idk lol

step-by-step explanation: