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Q.1.2

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The Practice of Statistics for AP

Found in: Page 698

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

Why is it important to compare proportions rather than counts in Question $1$ ?

Proportions have been computed to make the comparison and reach at the conclusion.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

The table is,

Step 2: Explanation

The proportion table is,

From the count table, it is known that there is a huge difference between the sample size of two campuses which makes the comparison impossible. Thus, proportions have been computed to make the comparison and reach at the conclusion.

Most popular questions for Math Textbooks

Refer to Exercises 1 and 3.

(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’s C2cdf command

(d) What conclusion would you draw about the company’s claimed distribution for its deluxe mixed nuts? Justify your answer.

$\begin{matrix} Use Facebook & Main Campus & Common wealth \\ Several times a month or less & 55 & 76 \\ At least once a week & 215 & 157 \\ At least once a day & 640 & 394 \\ Total Facebook users & 910 & 627 \end{matrix}$

Use Table C to find the $p$ -value. Then use your calculator’s $χ^{2} cdf$ command.

The Pennsylvania State University has its main campus in the town of State College and more than $20$ smaller “commonwealth campuses” around the state. The Penn State Division of Student Affairs polled separate random samples of undergraduates from the main campus and commonwealth campuses about their use of online social networking. Facebook was the most popular site, with more than $80 %$ of students having an account. Here is a comparison of Facebook use by undergraduates at the main campus and commonwealth campuses who have a Facebook account:

Calculate the conditional distribution (in proportions) of Facebook use for each campus setting?

Benford’s law Faked 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.^$3$ 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 $α = 0.05$ 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?

How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs and the number that hatched

(a) Make a two-way table of temperature by outcome (hatched or not). Calculate the proportion of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief?

(b) Are the differences between the three groups statistically significant? Give appropriate evidence to support your answer

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