Question

A sample of college students was asked how they felt about their weight. Of the 143 women in the sample who responded, 38 women said that they felt overweight, 99 felt that their weight was about right, and 6 felt that they were underweight. Of the 78 men in the sample, 18 men felt that they were overweight, 35 felt that their weight was about right, and 25 felt that they were underweight (Data source: pennstate3 dataset on the companion website).

a. In the relationship between feelings about weight and sex, which variable is the explanatory variable and which is the response variable?

b. Summarize the observed counts by creating a table similar to Tables 2.2 and 2.3 (p. 21).

c. For the 143 women, find the percentage responding in each category for how they felt about their weight.

d. For the 78 men, find the percentage responding in each category for how they felt about their weight.

e. Using the percentages found in parts (c) and (d), summarize how the women and men differed in how they felt about their weight.

Answer 1

a. Feelings about weight is the response (dependent) variable. Sex is the explanatory (independent) variable. The feelings about weight depend on the sex

b. Summary of observed counts

Women Men Total

Overweight 38 18 56

Right weight 99 35 134

Underweight 6 25 31

Number 143 78 221

c. Percentage of the 143 women responding in each category:

1. Overweight = 38/143 = 26.6%

2. Right weight = 99/143 = 69.2%

3. Underweight = 6/143 = 4.2%

d. Percentage of the 78 men responding in each category:

1. Overweight = 18/78 = 23.1%

2. Right weight = 35/78 = 44.9%

3. Underweight = 25/78 = 32%

e. Summary of feelings about weight:

Women Men

Overweight 26.6% 23.1%

Right weight 69.2% 44.9%

Underweight 4.2% 32%

Explanation:

a) Data:

Sample size = 221

Women Men Total

Overweight 38 18 56

Right weight 99 35 134

Underweight 6 25 31

Number 143 78 221

b) To obtain the percentage of feelings about weight for each category, the number of those who feel overweight, right weight, or underweight is divided by the total number of women or men. The value obtained, which is in decimal form, is then converted to percentage by multiplying with 100.