A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
What is the variance on this questionnaire in the general population?
To calculate the variance on the questionnaire in the general population, you need to use the formula for variance.
Variance (σ^2) is calculated as the squared difference between each value (X) and the mean (μ), summed up, and then divided by the total number of values (N).
In this case, you are given the mean (μ) of the general population, which is 60, and the standard deviation (σ), which is 16. However, you need to find the variance (σ^2).
To calculate the variance, square the standard deviation: σ^2 = σ * σ = 16 * 16 = 256.
Therefore, the variance on this questionnaire in the general population is 256.