Question

Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

Left-Handed

Right-Handed

Men

13

22

Women

27

18

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Handedness and gender are independent.
H_a: Handedness and gender are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
E_r,c = (n_r * n_c) / n

Χ² = Σ [ (O_r,c - E_r,c)² / E_r,c ]
Χ² = 4.114

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 4.114.

We use the Chi-Square Distribution Calculator to find P(Χ² > 4.114) = 0.0425

Interpret results. Since the P-value (0.0425) is less than the significance level (0.05), we cannot accept the null hypothesis.

Thus, we conclude that there is a relationship between Handedness and gender.