Question

the amount of time it takes students to travel to school can vary greatly depending on how far a student lives from the school and what mode of transportation they take to school. a student claims that the average travel time to school for his large district is 20 minutes. to further investigate this claim, he selects a random sample of 50 students from the school and finds that their mean travel time is 22.4 minutes with a standard deviation of 5.9 minutes. he would like to conduct a significance test to determine if there is convincing evidence that the true mean travel time for all students who attend this school is greater than 20 minutes. what are the appropriate hypotheses?

Answer 1

Answer: The appropriate hypotheses for this significance test are:

Null hypothesis (H0): The true mean travel time for all students who attend this school is equal to 20 minutes.

Alternative hypothesis (Ha): The true mean travel time for all students who attend this school is greater than 20 minutes.

The null hypothesis states that there is no difference between the claim (20 minutes) and the sample mean (22.4 minutes). The alternative hypothesis states that there is a difference and the sample mean is greater than the claim. The student will use the sample data and a chosen significance level (such as α = 0.05) to decide whether to reject or fail to reject the null hypothesis.

Explanation: