1. a student is interested in whether there i...
1. a student is interested in whether there is a relationship between gender and major at her college. she randomly sampled some men and women on campus and asked them if their major was part of the natural sciences (ns), social sciences (ss), or humanities (h). her results appear in the table below.\n| | ns | ss | h | total |\n|--|--|--|--|--|\n| women | 10 | 14 | 10 | 34 |\n| men | 11 | 8 | 4 | 23 |\n| total | 21 | 22 | 14 | 57 |\nwhat would be the expected frequency of women in social sciences based on this table?\na. 8.35\nb. 13.12\nc. 12.53\nd. 15.21
Answer
# Explanation:
## Step1: Recall expected - frequency formula
The formula for the expected frequency in a contingency - table is $E_{ij}=\frac{R_i\times C_j}{N}$, where $R_i$ is the row total, $C_j$ is the column total, and $N$ is the grand total.
For women in social sciences, $R_i$ (total number of women) = 34, $C_j$ (total number of social - science majors) = 22, and $N$ (grand total) = 57.
## Step2: Calculate the expected frequency
$E=\frac{34\times22}{57}=\frac{748}{57}\approx13.12$
# Answer:
B. 13.12