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Chapter 11: Q. 3.3 (page 705)
What conclusion would you draw? Justify your answer.
At significance level, there is enough evidence to state that there is a difference in the distribution of users in both the schools.
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Benford’s lawFaked numbers in tax returns, invoices, or expense account claims often display patterns that aren’t present in legitimate records. Some patterns are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford’s law. Call the first digit of a randomly chosen record X for short. Benford’s law gives this probability model for X (note that a first digit can’t be 0):
A forensic accountant who is familiar with Benford’s law inspects a random sample of invoices from a company that is accused of committing fraud. The table below displays the sample data.
(a) Are these data inconsistent with Benford’s law? Carry out an appropriate test at the level to support your answer. If you find a significant result, perform follow-up analysis.
(b) Describe a Type I error and a Type II error in this setting, and give a possible consequence of each. Which do you think is more serious?
The conditions for carrying out the chi-square test in exercise T11.2 are
I. Separate random samples from the populations of interest.
II. Expected counts large enough.
III. The samples themselves and the individual observations in each sample are independent.
Which of the conditions is (are) satisfied in this case?
(a) I only
(d) Il and III only
(b) II only
(e) I, II, and III
(c) I and II only
Market research Before bringing a new product to market, firms carry out extensive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent. The participants are a random sample of people who don’t currently use the established brand that the new product will compete with. Give subjects free samples of both detergents. After they have tried both for a while, ask which they prefer. The answers may depend on other facts about how people do laundry.
(a) How are laundry practices (water hardness and wash temperature) related to the choice of detergent? Make an appropriate graph to display this relationship. Describe what you see.
(b) Determine whether or not the sample provides convincing evidence that laundry practices and product preference are independent in the population of interest
Use Table C to find the -value. Then use your calculator’s command.
Orange, lemon, cherry, raspberry, blueberry, and lime are among the six fruit flavours available in Kellogg's Froot Loops cereal. Charise counted the number of cereal pieces in each flavour as she poured out her morning bowl of cereal. Here are her statistics.
Test the null hypothesis that each flavour of Kellogg's Froot Loops is distributed evenly throughout the population. Perform a follow-up analysis if you discover a noteworthy result.
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