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An ice cream maker performs a nationwide survey about favorite flavors of ice cream in different geographic areas of the U.S. Based on the Table, do the numbers suggest that geographic location is independent of favorite ice cream flavors? Test at the 5%significance level.

USRegionStraChocoVanRockyRoadMintChocolateChipPistachioTotalWest1221221915897Midwest1032221115696East83127815796South1528308156102Total45112101466027391

Short Answer

Expert verified

Taking α=0.05, we can see that p>α. This means that we cannot reject the null hypothesis.

Step by step solution

01

Given Information

The table with observed values:

StraChocoVanR RM C CPistTotalWest1221221915897Midwest1032221115696East83127815796South1528308156102Total45112101466027391

The table with expected values:

StraChocoVanR RM C CPistTotalWest11.1627.7925.05611.4114.886.797Midwest11.0527.524.811.2914.736.6396East11.0527.524.811.2914.736.6396South11.7429.2226.351215.657.04102Total45112101466027391

02

Explanation

We want to test the following hypotheses:

H0: Geographic location is independent of favorite ice cream flavors

H1: Geographic location depends on favorite ice cream flavors

Since there are 4regions and 6flavors, the number of degrees of freedom is

(4-1)(6-1)=15

We are using χ2distribution. The test statistic is given by:

χ2=∑i=14∑j=16Obi,j-Exi,j2Exi,j=14.06317

03

Graph

Using the applet for χ2distribution, we get that p-value is 0.52074:

Chi-Square Distribution

X~χ(df)2

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Most popular questions from this chapter

The table provides a recent survey of the youngest online entrepreneurs whose net worth is estimated at one million dollars or more. Their ages range from 17to 30. Each cell in the table illustrates the number of entrepreneurs who correspond to the specific age group and their net worth. Are the ages and net worth independent? Perform a test of independence at the 5%significance level.

Age Groupl Net Worth Value (in millions of US dollars)1-56-24≥25Row Total17-258752026-3065920Column Total14121440

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.

A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier.

U.S. Ski AreaBeginnerIntermediateAdvanced
Tahoe203040
Utah10
3060
Colorado1040 50

Table11.43

Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of \(200\) passengers is taken. Table 11.31 shows the results.

The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

What is the \(p-\)value?

The standard deviation of heights for students in a school is 0.81. A random sample of 50students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81.

What type of test should be used?

Students in a social studies class hypothesize that the literacy rates across the world for every region are \(82%\). Table 11.14 shows the actual literacy rates across the world broken down by region. What are the test statistic and the degrees of freedom?

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