Question

Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265. 1a. Explain what it would mean for the null hypothesis to be true in this setting. 1b . Interpret the p-value. 1c. What conclusion would you make at the alpha = 0.05 signifigance level?

Answer 1

1a. The null hypothesis in this setting would mean that the proportion of students who completed their math homework is equal to or greater than 75%.

1b. The p-value represents the probability of observing a sample proportion as extreme as or more extreme than the sample proportion observed (68%), given that the null hypothesis is true. In this case, the p-value of 0.1265 indicates that there is a 12.65% chance of observing a sample proportion as extreme or more extreme than 68%, assuming the true proportion is equal to or greater than 75%.

1c. At the alpha = 0.05 significance level, we reject the null hypothesis if the p-value is less than 0.05. In this case, the p-value of 0.1265 is greater than 0.05, meaning we fail to reject the null hypothesis. Therefore, at the alpha = 0.05 significance level, we cannot conclude that less than 75% of students completed their math homework.