A researcher wanted to know if a student’s book series preference was dependent

Question

A researcher wanted to know if a student’s book series preference was dependent upon the year they were in school. They collected data from 1000 students and asked them if the preferred the Harry Potter series, the Hunger games series, or the A Song of Ice and Fire series and what year they were in school. The results from the survey are below:

Book Preference

Year Harry Potter Hunger Games A Song of Ice and Fire Total

Freshman 125 ( ) 50 ( ) 75 ( ) 250

Sophomore 90 ( ) 120 ( ) 40 ( ) 250

Junior 60 ( ) 175 ( ) 15 ( ) 250

Senior 25 ( ) 75 ( ) 150 ( ) 250

Total 300 420 280 1000

In a separate word file, answer the following questions using complete sentences when applicable and copying and pasting the relevant charts, tables and graphs when appropriate.

1. Identify the population, the sample, and the variables from this study.

2. Identify the independent and the dependent variables from this study and why you identified them that way.

3. In the space below, calculate the expected values for each cell in the contingency table and write those values in the parentheses in the data table above (show all of you work).

4. Using = 0.05, perform a chi-square test to answer the researcher’s question. Write up your conclusion.

Explanation / Answer

A researcher wanted to know if a student’s book series preference was
dependent upon the year they were in school
a.
total no.of students they were in school is the population and the study of 1000 students
who randomly picked is the sample  

b.
book series preference is the dependent variable and year of study is the
indepdndent variable

c.
Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: book series preference is independent on year of study

alternative, H1: book series preference is dependent on year of study

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =12.592

since our test is right tailed,reject Ho when ^2 o > 12.592

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 306.714

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 3 - 1 ) = 3 * 2 = 6 is 12.592

we got | ^2| =306.714 & | ^2 | =12.592

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0

ANSWERS

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null, Ho: book series preference is independent on year of study

alternative, H1: book series preference is dependent on year of study

test statistic: 306.714

critical value: 12.592

p-value:0

decision: reject Ho

have evidence thtat book series preference is dependent on year of study

MATRIX col1 col2 col3 TOTALS row 1 125 50 75 250 row 2 90 120 40 250 row 3 60 175 15 250 row 4 25 75 150 250 TOTALS 300 420 280 1000

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