/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 1. Aw, nuts! A company claims that ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Q 1. (page 712)

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 table displays the sample data.

a. State appropriate hypotheses for performing a test of the company鈥檚 claim.

b. Calculate the expected count for each type of nut.

c. Calculate the value of the chi-square test statistic.

Short Answer

Expert verified

Part (a)H0:pc=52%,pa=27%,pm=13%,pb=8%,Ha:Atleastoneofthepi鈥�sisincorrect.

Part (b)

Type of nutsCountFrequencyExpected
Cashew8352%78
Almond2927%40.5
Macadamia2013%19.5
Brazil188%12
Total150100%150

Part (c) The chi-square test statistic =6.60

Step by step solution

01

Part (a) Step 1: Given information

Type of nutCountFrequency
Cashew8352%
Almond2927%
Macadamia2013%
Brazil188%
02

Part (a) Step 2: Explanation

The null and alternative hypotheses:

H0:pc=52%,pa=27%,pm=13%,pb=8%,Ha:Atleastoneofthepi鈥�sisincorrect.

03

Part (b) Step 1: Explanation

Expectedvalue=n脳frequency

Where, n=150

Expected count will be:

Type of nutsCountFrequencyExpected
Cashew8352%78
Almond2927%40.5
Macadamia2013%19.5
Brazil188%12
Total150100%150
04

Part (c) Step 1: Explanation

Using excel

Type of nutsObservedExpectedO-E
O-E2/E
% of chisq
Cashew8378.0005.0005.0004.86
Almond2940.500-11.5003.26549.49
Macadamia2019.5000.5000.0130.19
Brazil1812.0006.0003.00045.46

150150.0000.0006.599100.00







6.60chi-square



3Df



.0858p-value


Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees.

a. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they鈥檙e searching for seeds and insects?

b. Relative to the proportion of each tree type in the forest, which type of trees do the nuthatches seem to prefer the most? The least?

Spinning heads? When a fair coin is flipped, we all know that the probability the coin lands on heads is 0.50 However, what if a coin is spun? According to the article 鈥淓uro Coin Accused of Unfair Flipping鈥� in the New Scientist, two Polish math professors and their students spun a Belgian euro coin 250 times. It landed heads 140 times. One of the professors concluded that the coin was minted asymmetrically. A representative from the Belgian mint indicated the result was just chance. Assume that the conditions for inference are met.

a. Carry out a chi-square test for goodness of fit to test if heads and tails are equally likely when a euro coin is spun.

b. In Chapter 9 Exercise 50 you analyzed these data with a one-sample z test for a proportion. The hypotheses were H0:p=0.5 and Ha:p鈮�0.5

where p=the true proportion of heads. Calculate the z statistic and P-value for this test. How do these values compare to the values from part (a)?

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100students and asks them, 鈥淲hich type of food do you prefer: Ramen, tacos, pizza, or hamburgers?鈥� Here are her data:

The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?

a. Because 0.0129 is less than 伪=0.05 reject H0 . There is convincing evidence that the food choices are equally popular.

b. Because 0.0129 is less than 伪=0.05 reject H0 There is not convincing

evidence that the food choices are equally popular.

c. Because 0.0129 is less than 伪=0.05 reject H0 . There is convincing evidence that the food choices are not equally popular.

d. Because 0.0129 is less than 伪=0.05 fail to reject H0 There is not convincing evidence that the food choices are equally popular.

e. Because 0.0129 is less than 伪=0.05 fail to reject H0 There is convincing

evidence that the food choices are equally popular.

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test H0: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

We compute the value of the 蠂2test statistic to be 6.57. Assuming that the conditions for inference are met, which of the following is the correct P-value?

a. Greater than0.20

b. Between 0.10and0.20

c. Between 0.05and0.10

d. Between 0.01and0.05

e. Less than0.01

More candy The two-way table shows the results of the experiment

described in Exercise 27.


Red SurveyBlue Survey
Control Survey
Total
Red Candy13
5
8
26
Blue Candy
7
15
12
34
Total20
20
20
60

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Red/Red cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.