.In a sample of 47 adults selected randomly from one town, it is found that 9 of them havebeen exposed to a particular strain of the flu. Test the claim that the proportion of alladults in the town that have been exposed to this strain of the flu is 8%.a)State null and alternative hypothesis. Also denote the claim.

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people exposed to flu is different from 0.08 or 8%

Step-by-step explanation:

Data given and notation

n=47 represent the random sample taken

X=9 represent the number of people exposed to flu

[tex]\hat p=\frac{9}{47}=0.191[/tex] estimated proportion of people exposed to flu

[tex]p_o=0.08[/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 proportion of people exposed to flu is 0.08.:

Null hypothesis:[tex]p=0.08[/tex]

Alternative hypothesis:[tex]p \neq 0.08[/tex]

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

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

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

Calculate the statistic

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

[tex]z=\frac{0.191 -0.08}{\sqrt{\frac{0.08(1-0.08)}{47}}}=2.805[/tex]

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 assumed is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

[tex]p_v =2*P(z>2.805)=0.005[/tex]

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people exposed to flu is different from 0.08 or 8%