We are conducting a hypothesis test to determine if fewer than 80% of st 311 hybrid students complete all modules before class. our hypotheses are h0 : p = 0.8 and ha : p < 0.8. we looked at 110 randomly selected students and found that 97 of these students had completed the modules before class. what is the appropriate conclusion for this test?

Null hypothesis:  

Alternative hypothesis:  

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

So the p value obtained was a very high value and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:  

Alternative hypothesis:

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.

Step-by-step explanation:

1) Data given and notation  

n=110 represent the random sample taken

X=97 represent the students who completed the modules before class

estimated proportion of students who completed the modules before class

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

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 .

3) Calculate the statistic  

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

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

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

So the p value obtained was a very high value and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis:  

Alternative hypothesis:

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.

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step-by-step explanation:

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