Question

a textbook company states that the average time a student needs to take a quiz from its book is 30 minutes with a standard deviation of 3 minutes. a teacher using the book is not sure that this is correct for her classes and wants to check. she collects data on 10 random students and finds that the average time to take the quiz was only 25 minutes. as a result, the teacher performs a two - tailed hypothesis test with a significance level of 5%. which conclusion is valid based on the results of the test?
her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.
the teacher should pick up all unfinished quizzes at 25 minutes because her students are so much faster than average.
the teacher does not have enough information to make a conclusion about the average time on the test.
her students, on average, do take the 30 minutes as the textbook company stated.

Explanation:

To solve this, we analyze the hypothesis test. The textbook company claims the average time (μ) is 30 minutes. The teacher's sample of 10 students has a sample mean of 25 minutes. A two - tailed hypothesis test at a 5% significance level is performed. If the p - value (or test statistic result) leads to rejecting the null hypothesis (H₀: μ = 30), we conclude that the average time is not 30 minutes. The second option is incorrect as hypothesis testing about the mean doesn't dictate when to collect quizzes. The third option is incorrect as we do have enough info (sample mean, population standard deviation, sample size, significance level) to perform the test. So, if we reject H₀, we conclude the students' average time is not 30 minutes.

Answer:

Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated.