Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Q. 29 (page 753)

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.

Short Answer

Expert verified

(a)Null hyptheses:The true distributions of color choice are not different for the three types of surveys.

Alternative hyptheses: The true distributions of color choice are different for the three types of surveys.

(b)The expected count in Red/Red cell =8.67

(c)The value of the chi-square test statistic =6.62

Step by step solution

01

Part (a) Step 1:Given Information

We have been given that,


Red Survey
Blue Survey
Control Survey
Total
Red Candy
13
5
8
26
Blue Candy
7
15
12
34
Total
20
20
20
60
02

Part (a) Step 2:Explanation

Null hyptheses:The true distributions of color choice are not different for the three types of surveys.

Alternative hyptheses: The true distributions of color choice are different for the three types of surveys.

03

Part (b) Step 1:Given Information

We have been given that,


Red Survey
Blue Survey
Control Survey
Total
Red Candy
13
5
8
26
Blue Candy
7
15
12
34
Total
20
20
20
60
04

Part (b) Step 2:Explanation

The expected count is calculated as:RowTotal*ColumnTotalGrandTotal

So, The expected count in Red/Red cell =26*2060=8.678.67

Table of expected counts :


Red Survey
Blue Survey
Control Survey
Red Candy
8.67
8.67
8.67
Blue Candy
11.33
11.33
11.33
05

Part (c) Step 1:Given Information

We have been given that,


Red Survey
Blue Survey
Control Survey
Total
Red Candy
13
5
8
26
Blue Candy
7
15
12
34
Total
20
20
20
60
06

Part (c) Step 2:Explanation

Here,

fo=observed count

fe=expected count

fofefo-fe(fo-fe)2(fo-fe)2/fe
13
8.67
4.33
18.74
2.16
711.33
-4.33
18.74
1.65
5
8.67
role="math" localid="1654163603493" -3.67
13.46
1.55
15
11.33
3.67
13.46
1.18
8
8.67
-0.67
0.44
0.05
12
11.33
0.67
0.44
0.03




Chi-Square value:6.62

Calculated chi-square value :6.62

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Roulette Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 slots—18 red, 18 black, and 2 green. In one casino, managers record data from a random sample of 200 spins of one of their American roulette wheels. The table displays the results.

a. State appropriate hypotheses for testing whether these data give convincing evidence that the distribution of outcomes on this wheel is not what it should be.

b. Calculate the expected count for each color.

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

No chi-square A school’s 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 50 students 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 test for goodness of fit using these data.

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, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

The chi-square test 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

Opinions about the death penaltyThe General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor or oppose the death penalty for persons convicted of murder?” Of the 1379people with only a high school degree, 1010 favored the death penalty, while 319of the 504people with a bachelor’s degree favored the death penalty. We can test the hypothesis of “no difference” in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.

a. State appropriate hypotheses for a chi-square test.

b. Here is Minitab output for a chi-square test. Interpret the P-value. What conclusion would you draw?

c. Here is Minitab output for a two-sample z test. Explain how these results are consistent with the test in part (a).

Going nuts The UR Nuts Company sells Deluxe and Premium nut mixes, both of which

contain only cashews, Brazil nuts, almonds, and peanuts. The Premium nuts are much

more expensive than the Deluxe nuts. A consumer group suspects that the two nut mixes

are really the same. To find out, the group took separate random samples of pounds of

each nut mix and recorded the weights of each type of nut in the sample. Here are the

data:

Explain why we can’t use a chi-square test to determine whether these two distributions

differ significantly.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

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.

Sign-up for free