Conduct a chi-square test of independence to determine if there is evidence of a

Question

Conduct a chi-square test of independence to determine if there is evidence of a relationship between gender and higher SAT score in the population of all STAT 200 students. Use the five-step hypothesis testing procedure. (Minitab)

i.Step 1: Check assumptions and write hypotheses.

ii.Step 2: Calculate an appropriate test statistic.

iii.Step 3: Determine the p-value.

iv.Step 4: Make a decision.

v.Step 5: State a “real world” conclusion.

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Explanation / Answer

i.Step 1: Check assumptions and write hypotheses.

H0: There is no association between Gender and HigherSAT score

H0: There is association between Gender and HigherSAT score

ii.Step 2: Calculate an appropriate test statistic.

First we prepare cross table from the given data

Tabulated statistics: HigherSAT, Gender

Rows: HigherSAT Columns: Gender

F M All

Math 83 126 209
Verbal 86 67 153
All 169 193 362

Chi-Square Test: F, M

Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts

F M Total
1 83 126 209
97.57 111.43
2.176 1.906

2 86 67 153
71.43 81.57
2.973 2.603

Total 169 193 362

Chi-Sq = 9.658, DF = 1,

iii.Step 3: Determine the p-value.

P-Value = 0.002

iv.Step 4: Make a decision.

Here P-value < alpha 0.05, we reject H0

v.Step 5: State a “real world” conclusion.

We conclude that There is association between Gender and HigherSAT score

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