Suppose that 34% of the students at a university favor the semester system, 61% favor the quarter system, and 5% have no preference. Is a random sample of 100 students large enough to provide convincing evidence that the quarter system is favored

So the p value obtained was a very low value and using the significance level assumed 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 students who favor the quarter system is higher than 0.5

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

estimated proportion of interest

is the value that we want to test

represent the significance level

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 true proportion for quarter system is higher than 0.5.:  

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

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

So the p value obtained was a very low value and using the significance level assumed 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 students who favor the quarter system is higher than 0.5

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step-by-step explanation: