Giving out 100 fg for quick statistic questions
If you use R Commander to compute probabilities for any of the questions, please state clearly you have
done so and provide parameter values that you input in R Commander.
1. In large introductory statistics courses, clicker is commonly used in lectures. For all students enrolled in
large introductory statistics courses, their clicker response times have a mean of 1 minute and a standard
deviation of 0.2 minutes.
(a) What is the probability that a randomly selected student needs more than 1.2 minutes to answer a
clicker question? Do you need to assume a distribution for the response times in order to compute this
probability? If so, clearly state what it is. If not, explain why not. (2 marks)
(b) Suppose that the instructor closes the poll for a clicker question whenever he sees that 95% of students
have responded. What is the longest time a student can take to respond to a clicker question and have
his/her answer recorded (answers submitted after the poll closes will not be recorded)? Do you need
to assume a distribution for the response times for this calculation? If so, clearly state what it is. If
not, explain why not. (3 marks)
(c) An introductory statistics class has regular group activities where each group consists of four students.
What is the probability that a randomly selected group from the class needs more than an average of
1.2 minutes to answer a clicker question? Do you need to assume a distribution for the response times
for this calculation? If so, clearly state what it is. If not, explain why not. (3 marks)
(d) A lab section of an introductory statistics course has 30 students. What is the probability that all the
students in this lab section needs more than an average of 1.2 minutes to answer a clicker question?
Assume that the 30 students are representative of all students enrolled in the course. Do you also need
to assume a distribution for the response times for this calculation? If so, clearly state what it is. If
not, explain why not. (3 marks)
(e) Consider the following two distributions:
(1) the distribution of the response times of 30 students randomly chosen from a course
(2) the distribution of the average response time of 30 students randomly chosen from a course
Comment on any differences between these two distributions (in terms of their center, spread and
shape) and briefly explain why. (4 marks)
2. In-class activities are becoming more common in lectures. Previous studies show that at least 60% of
students like in-class activities. An instructor is suspicious about this claim and thinks that the claim is
exaggerated. Thus, he decides to conduct a study in the class he is currently teaching. His class has 100
students, and he finds that 55 students like in-class activities based on a recent survey.
(a) Construct a 95% confidence interval for the true percentage of all students who like in-class activities
based on the current study. Also provide an interpretation to the confidence interval. (3 marks)
(b) Is there sufficient evidence to support the instructor’s suspicion based on the current study? Conduct
an appropriate hypothesis test. Remember to state the hypotheses, compute the P-value and state
any assumption that you need to conduct the hypothesis test. You must define all notation that you
use. (6 marks)
(c) Is your finding from (b) statistically significant at the 5% significance level? At the 10% level? Draw
an appropriate conclusion in the context of this question. (2 marks)
(d) Do you have any reservations about your conclusions in (c)? Is there any way to improve the design
of the study? (2 marks)
(e) Describe the Type II error of the hypothesis test in the context of this question. (1 mark)
(f) What is the probability that the finding from previous studies holds but you reject the finding based
on the current study at the 5% significance level? (1 mark)