The table to the right contains observed values and expected values in parenthes

Question

The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below.

(a) Compute the value of the chi-square test statistic.

chi Subscript 0 Superscript 2=?

(b) Test the hypothesis that X and Y are independent at the

alpha equals 0.05

level of significance.

A.Upper H 0: The Upper Y category and Upper X category are independent.

Upper H 1: The Upper Y category and Upper X category are dependent.

B.Upper H 0: The Upper Y category and Upper X category have equal proportions.

Upper H 1:The proportions are not equal.

C.Upper H 0: The Upper Y category and Upper X category are dependent.

Upper H 1: TheUpper Y category and Upper X category are independent.

D.Upper H 0: mu Subscript x equals Upper E Subscript xand mu Subscript y equals Upper E Subscript y

Upper H 1: mu Subscript x not equals Upper E Subscript xor mu Subscript y not equals Upper E Subscript y

What is the P-value?

P-value=?

Should the null hypothesis be rejected?

A.No, do not reject Upper H 0. There is sufficient evidence at the alpha equals0.05level of significance to conclude that X and Y are dependent because the P-valueless than alpha.

B.No, do not reject Upper H 0. There is not sufficient evidence at the alpha equals0.05level of significance to conclude that X and Y are dependent because the P-valuegreater than alpha.

C.Yes, reject Upper H 0. There is not sufficient evidence at the alpha equals0.05level of significance to conclude that X and Y are dependent because the P-valuegreater than alpha.

D.Yes, reject Upper H 0. There is not sufficient evidence at the alpha equals0.05level of significance to conclude that X and Y are dependent because the P-value less than alpha.

_ X1 X2 X3 Y1 32 (33.33) 44 (45.83) 49 (45.83) Y2 16 (14.67) 22 (20.17) 17 (20.17)

Explanation / Answer

solutionA:

chisq=1.13

A.Upper H 0: The Upper Y category and Upper X category are independent.

Upper H 1: The Upper Y category and Upper X category are dependent.

Df=(r-1)(c-1)

=(2-1)(3-1)

r is no of rows c is no of columns

=1.2

df =2

alpha=0.05

p=0.5682

p>0.05

Fail to reject Null hypothesis

Accept Null hypothesis.

B.No, do not reject Upper H 0. There is not sufficient evidence at the alpha equals0.05level of significance to conclude that X and Y are dependent because the P-valuegreater than alpha

O E O-E (O-E)^2 (O-E)^2/E 32 33.33 -1.33 1.7689 0.053072 44 45.83 -1.83 3.3489 0.073072 49 45.83 3.17 10.0489 0.219265 16 14.67 1.33 1.7689 0.120579 22 20.17 1.83 3.3489 0.166034 17 20.17 -3.17 10.0489 0.49821 CHISQSTATISTIC 1.130233

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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