Question

you ask 100 of your classmates if they like winter. there are 15 girls who like winter, 25 who do not, and 5 with no opinion. there are 20 boys who like winter, 10 who do not, and 25 with no opinion. construct a two-way frequency table to show the results of the survey. complete parts a through c.

table with columns: like winter? (yes, no, no opinion, total) and gender (girls, boys, total) with values: yes - girls:15, boys:20, total:35; no - girls:25, boys:10, total:35; no opinion - girls:5, boys:25, total:30; total - girls:45, boys:55, total:100

b. does one group like winter more than the other? explain. select the correct answer below and fill in the answer boxes to complete your choice.
○ a. yes. girls seem to like winter more because □ out of □ girls responded \yes\ or
o opinion,\ and □ out of □ boys responded \yes\ or
o opinion.\
○ b. yes. boys seem to like winter more because □ out of □ boys responded \yes\ or
o opinion,\ and □ out of □ girls responded \yes\ or
o opinion.\
○ c. no. neither group seems to like winter more because □ out of □ girls responded \yes\ or
o opinion,\ and □ out of □ boys responded \yes\ or
o opinion.\

Explanation:

Step1: Calculate "Yes" or "No Opinion" for girls

Girls who said "Yes": 15, "No Opinion": 5. Sum: \( 15 + 5 = 20 \). Total girls: 45.

Step2: Calculate "Yes" or "No Opinion" for boys

Boys who said "Yes": 20, "No Opinion": 25. Sum: \( 20 + 25 = 45 \). Total boys: 55. Wait, no—wait, the correct approach: Wait, the option B says boys seem to like more. Wait, let's recalculate. Wait, "Yes" or "No Opinion" for girls: 15 (Yes) + 5 (No Opinion) = 20. Total girls: 45. For boys: 20 (Yes) + 25 (No Opinion) = 45? No, wait 20 +25=45? But total boys are 55. Wait, no, the table: Girls total is 45 (15+25+5=45), boys total 55 (20+10+25=55). So "Yes" or "No Opinion" for girls: 15 +5=20. For boys: 20 +25=45. Wait, but 45 out of 55 boys, and 20 out of 45 girls. Wait, no, maybe I misread. Wait, the question is "Does one group like winter more than the other?". Let's check the proportion. For girls: "Yes" is 15/45 = 1/3 ≈ 0.333. For boys: 20/55 ≈ 0.363. Alternatively, "Yes" or "No Opinion" (maybe the question is about positive or neutral). Wait, the option B: Boys seem to like more because [boys' Yes or No Opinion] out of [boys' total], and [girls' Yes or No Opinion] out of [girls' total]. So boys: 20 (Yes) +25 (No Opinion)=45. Total boys:55. Girls:15 (Yes)+5 (No Opinion)=20. Total girls:45. Wait, 45 out of 55 boys, 20 out of 45 girls. Wait, 45/55 ≈ 0.818, 20/45 ≈ 0.444. So boys have higher. So fill in: 45 out of 55 boys, 20 out of 45 girls.

Answer:

For option B: 45 out of 55 boys responded "Yes" or "No Opinion," and 20 out of 45 girls responded "Yes" or "No Opinion." So the filled boxes are: 45, 55, 20, 45. And the answer is B. Yes. Boys seem to like winter more because 45 out of 55 boys responded "Yes" or "No Opinion," and 20 out of 45 girls responded "Yes" or "No Opinion."