Please complete the following questions. (13 pts) A researcher would like to tes

Question

Please complete the following questions.

(13 pts) A researcher would like to test whether age and college major are independent. He creates three age groups, "teens", "twenties", and "thirties" and goes to 2 classrooms in his local university: English Lit and Calculus 101. He counts the number of students falling into each age group for both classes; the data are below (use alpha.05 to test his hypothesis). 7. Thirties English Calculus Teens 13 31 Twenties 27 19 8 (2 pts) What test is appropriate for this analysis? a. b. (1 pt) State the null hypothesis: c. (1 pt) State the alternative hypothesis: (2 pts) Find the critical value: (3 pts) Calculate the test statistic: (2 pts) Make a decision: (2pts) What does your decision mean? d. e. f. g.

Explanation / Answer

Given table data is as below

------------------------------------------------------------------

calculation formula for E table matrix

------------------------------------------------------------------

expected frequecies calculated by applying E - table matrix formulae

------------------------------------------------------------------

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

------------------------------------------------------------------

set up null vs alternative as

null, Ho: age and college major are independent

alternative, H1: age and college major are dependent

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =5.991

since our test is right tailed,reject Ho when ^2 o > 5.991

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

from the table , ^2 o = 17.963

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991

we got | ^2| =17.963 & | ^2 | =5.991

make decision

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

^2 p_value =0

ANSWERS

---------------

null, Ho: age and college major are independent

alternative, H1: age and college major are dependent

test statistic: 17.963

critical value: 5.991

p-value:0

decision: reject Ho

we have evidence that age and college major are dependent

MATRIX col1 col2 col3 TOTALS row 1 13 27 19 59 row 2 31 11 8 50 TOTALS 44 38 27 N = 109

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.