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Chapter 11: Q.9 (page 692)

No chi-square A school鈥檚 principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night:

Explain carefully why it would not be appropriate to perform a chi-square goodness-of-铿乼 test using these data.

Short Answer

Expert verified

From the given information, You can only apply the chi-square goodness-of-fit test to categorical variables, but the variable is quantitative and thus it is not appropriate to apply the chi-square goodness-of-fit test.

Step by step solution

01

Given Information

It is given in the question that,

02

Explanation

The variable of interest here is the average amount of time that can take quantitative values, and the chi-square goodness of fit test is used on the category variable, with quantitative variables. As a result, chi-square goodness of fit cannot be used in this case.

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Most popular questions from this chapter

Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, 128seagulls landed on the sand, role="math" localid="1650465230449" 61landed in the mud, and role="math" localid="1650465221489" 11landed on the rocks. Carry out a chi-square goodness-of-铿乼 test. What do you conclude?

The chi-square statistic is

(a) (18-25)225+(22-25)225+(39-25)225+(21-25)225

(b) (25-18)218+(25-22)222+(25-39)239+(25-21)221

(c) (18-25)25+(22-25)25+(39-25)25+(21-25)25

(d)(18-25)2100+(22-25)2100+(39-25)2100+(21-25)2100

(e)(0.18-0.25)20.25+(0.22-0.25)20.25+(0.39-0.25)20.25+(0.21-0.25)20.25

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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.

Refer to Exercises 2 and 4.

(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?

(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.

(c) Use Table C to find the P-value. Then use your calculator鈥檚 C2cdf command.

(d) What conclusion would you draw about whether the roulette wheel is operating correctly? Justify your answer

Benford鈥檚 lawFaked numbers in tax returns, invoices, or expense account claims often display patterns that aren鈥檛 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 铿乺st digits of numbers in legitimate records often follow a model known as Benford鈥檚 law.3 Call the 铿乺st digit of a randomly chosen record X for short. Benford鈥檚 law gives this probability model for X (note that a 铿乺st digit can鈥檛 be 0):

A forensic accountant who is familiar with Benford鈥檚 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鈥檚 law? Carry out an appropriate test at the 伪=0.05level to support your answer. If you 铿乶d a signi铿乧ant result, perform follow-up analysis.

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