Dropouts A Statistics professor has observed that forseveral years about 13% of the students who initiallyenroll in his Introductory Statistics course withdrawbefore the end of the semester. A salesman suggests thathe try a statistics software package that gets studentsmore involved with computers, predicting that it will cut the dropout rate. The software is expensive, and the sales-man offers to let the professor use it for a semester to see if the dropout rate goes down significantly. The professorwill have to pay for the software only if he chooses tocontinue using it.a) Is this a one-tailed or two-tailed test? Explain.b) Write the null and alternative hypotheses.c) In this context, explain what would happen if theprofessor makes a Type I error.d) In this context, explain what would happen if theprofessor makes a Type II error.e) What is meant by the power of this test?
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!
several years about 13% of the students who initially
enroll in his Introductory Statistics course withdraw
before the end of the semester. A salesman suggests that
he try a statistics software package that gets students
more involved with computers, predicting that it will cut
man offers to let the professor use it for a semester to see
will have to pay for the software only if he chooses to
continue using it.
a) Is this a one-tailed or two-tailed test? Explain.
b) Write the null and alternative hypotheses.
c) In this context, explain what would happen if the
professor makes a Type I error.
d) In this context, explain what would happen if the
professor makes a Type II error.
e) What is meant by the power of this test?
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