Each of 40 subjects tastes two unmarked cups of coffee and says which he or she prefers. One cup in each pair contains instant coffee, the other fresh-brewed coffee. 30 of the subjects prefer the fresh-brewed coffee. Take p to be the proportion of the population who would prefer fresh-brewed coffee in a blind tasting. Test the claim that a majority of people prefer the taste of fresh-brewed coffee.

H0:P=__,HA:P>__
The test statistic is__ (2 decimals)
The p-value is__(4 decimals)
Therefore, at the ? = 0.05 level we can conclude that The data (does/ does not) provides statistical evidence that the majority of tasters (do/do not)prefer the fresh-brewed coffee.

Null hypothesis:  

Alternative hypothesis:

So the p value obtained was a very low value and using the significance level given we have 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 the subjects prefer the fresh-brewed coffee is higher than 0.5 (majority)

The data (does) provides statistical evidence that the majority of tasters (do) prefer the fresh-brewed coffee.

Step-by-step explanation:

Data given and notation

n=40 represent the random sample taken

X=30 represent the subjects prefer the fresh-brewed coffee

estimated proportion of the subjects prefer the fresh-brewed coffee

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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 majoriy of subjects prefer the fresh-brewed coffee.:  

Null hypothesis:  

Alternative hypothesis:  

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

(1)  

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

Calculate the statistic  

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

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 . The next step would be calculate the p value for this test.  

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

So the p value obtained was a very low value and using the significance level given we have 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 the subjects prefer the fresh-brewed coffee is higher than 0.5 (majority)

The data (does) provides statistical evidence that the majority of tasters (do) prefer the fresh-brewed coffee.