Suppose that the sample proportion of students who did all their assigned homework last week is $\hat{p}=\frac{57}{100}=0.57$. Would this sample proportion provide convincing evidence that less than $60\%$of all students at the school completed all their assigned homework last week? Explain your reasoning.

We have been given that the sample proportion of students who did all their assigned homework last week is $\hat{p}=\frac{57}{100}=0.57$

The sample proportion ($\hat{p}$) refers to the percentage of people in a sample who have a particular attribute or trait. The sample proportion is the percentage of successful samples; to calculate it, divide the number of people (or objects) who have the desired feature by the total number of persons (or items) in the sample.

Because $\frac{78}{250}=31.27\%$, of the values of $\hat{p}$in the simulation are less than or equal to $0.57$, a sample fraction of $\hat{p}=0.57$or less in an SRS of size $100$from a population with p =$0.60$ would not be surprising. A sample proportion of $\hat{p}\le 0.57$does not provide convincing evidence that the population proportion of students who completed all of their assigned homework is less than $\hat{p}=60\%$.

The disparity between the observed proportion ($\hat{p}=0.57$) and the proportion stated (p =$0.60$) could be explained by sampling variability.