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The Practice of Statistics for AP

Found in: Page 692

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains $52 %$ cashews, $27 %$ almonds, $13 %$ macadamia nuts, and 8% brazil nuts. To test this claim, a quality control inspector takes a random sample of $150$ nuts from the latest batch. The one-way table below displays the sample data.
(a) State appropriate hypotheses for performing a test of the company’s claim.
b) Calculate the expected counts for each type of nut. Show your work.

(a) The null hypothesis will be $H_{0}$ : The observed count of each type of nuts in a group of $150$ nuts from latest batch are same as claimed count of nuts in a group of $150$

Versus

$H_{1}$ : The observed counts of each type of nuts in a group of $150$ nuts from latest batch are not same as claimed count of nuts in a group of $150$ .

(b)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1:

The hypotheses for performing a test of company's claim that each batch of its deluxe mixed nuts contains $52 %$ cashews, $27 \%$ almonds, $13 \%$ macadamia and $8 \%$ brazil nuts whereas a random sample of 150 nuts from each batch is having the following composition.

Most popular questions for Math Textbooks

The degrees of freedom for the chi-square test for this two-way table are (a) $4$ .

(b) $8$ .

(c) $10$ .

(d) $20$ .

(e) None of these.

Gregor Mendel (1822–1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of $3$ smooth peas for every 1 wrinkled pea. In one experiment, he observed $423$ smooth and $133$ wrinkled peas. The data were produced in such a way that the Random and Independent conditions are met. Carry out a chi-square goodness-of-fit test based on Mendel’s prediction. What do you conclude?

Why men and women play sports Do men and women participate in sports for the same reasons? One goal for sports participants is social comparision—the desire to win or to do better than other people. Another is mastery—the desire to improve one’s skills or to try one’s best. A study on why students participate in sports collected data from independent random samples of 67 male and 67 female under-graduates at a large university 15 Each student was classified into one of four categories based on his or her responses to a questionnaire about sports goals. The four categories were high social comparison– high mastery (HSC-HM), high social comparison– low mastery (HSC-LM), low social comparison–high mastery (LSC-HM), and low social comparison–low mastery (LSC-LM). One purpose of the study was to compare the goals of male and female students. Here are the data displayed in a two-way table: Observed Counts for Sports Goals

(a) Check that the conditions for performing the chi-square test are met.

(b) Use Table C to find the P-value. Then use your calculator’s C2cdf command.

(c) Interpret the P-value from the calculator in context.

(d) What conclusion would you draw? Justify your answer.

The category that contributes the largest component to the $χ^{2}$ statistic is

(a) White.

(c) Hispanic.

(b) Black.

(d) Other.

(e) The answer cannot be determined since this is only a sample.

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

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