A statistics instructor would like to know whether it is worthwhile to require students to do weekly homework assignments. For one section of the statistics course, homework is assigned, collected and graded each week. For another section, the same problems are suggested each week, but the students are not required to turn in their homework. At the end of the semester, all students take the same final exam. The score distribution for the two sections are as follows: With Homework 12 15 17 5 10 No Homework 12 21 28 25 14 Do these data indicate a significant difference between the score distributions for students with homework versus students with no homework? Test at the 5% level of significance.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
- A statistics instructor would like to know whether it is worthwhile to require students to do weekly homework assignments. For one section of the statistics course, homework is assigned, collected and graded each week. For another section, the same problems are suggested each week, but the students are not required to turn in their homework. At the end of the semester, all students take the same final exam. The score distribution for the two sections are as follows:
With Homework 12 15 17 5 10
No Homework 12 21 28 25 14
Do these data indicate a significant difference between the score distributions for students with homework versus students with no homework? Test at the 5% level of significance.
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