Questions: College major and gender are dependent. College major and gender are independent. The distribution of college major is not the same for each gender. The distribution of college major is the same for each gender. The test-statistic for this data =4.123 (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.) The p-value is Select an answer Based on this, we should reject the null fail to reject the null accept the null Thus, the final conclusion is... There is insufficient evidence to conclude that college major and gender are dependent. There is sufficient evidence to conclude that college major and gender are dependent. There is sufficient evidence to conclude that college major and gender are independent. There is sufficient evidence to conclude that the distribution of college major is not the same for each gender. There is insufficient evidence to conclude that the distribution of college major is not the same for each gender.

Solution Steps

We are testing the relationship between college major and gender. The null and alternative hypotheses are defined as follows:

• \( H_0 \): College major and gender are independent.
• \( H_1 \): College major and gender are dependent.

The test statistic calculated for this data is given as:

\[ \text{Test Statistic} = 4.123 \]

The degrees of freedom for the Chi-Square test is calculated using the formula:

\[ \text{Degrees of Freedom} = (r - 1)(c - 1) \]

where \( r \) is the number of rows (categories of gender) and \( c \) is the number of columns (categories of college major). In this case, we have:

\[ \text{Degrees of Freedom} = (2 - 1)(3 - 1) = 2 \]

Using the Chi-Square distribution, the p-value corresponding to the test statistic is calculated as:

\[ \text{P-Value} = 1 - \chi^2_{\text{cdf}}(4.123, 2) \approx 0.1273 \]

The significance level \( \alpha \) is set at \( 0.05 \). We compare the p-value with \( \alpha \):

\[ \text{If } \text{P-Value} < \alpha \text{, reject } H_0; \text{ otherwise, fail to reject } H_0. \]

In this case:

\[ 0.1273 > 0.05 \implies \text{fail to reject } H_0 \]

Based on the comparison, we conclude that there is insufficient evidence to support the claim that college major and gender are dependent. Thus, we state:

\[ \text{Final Conclusion: There is insufficient evidence to conclude that college major and gender are dependent.} \]

Final Answer