Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures academic motivation and study habits. The SSHA score F of a randomly selected female student at a large university has mean 120 and standard deviation 28, and the SSHA score M of a randomly selected male student at the university has mean 105 and standard deviation 35. Suppose we select one male student and one female student at random from this university and give them the SSHA test. Calculate and interpret the mean of the difference $\mathrm{D}=\mathrm{F}-\mathrm{M}$in their scores.

Short answer

The difference's mean is$\mathrm{\mu }=15$

Step-by-step solution

Given information

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{F}}=120 \\ {\mathrm{\sigma }}_F=28 \\ {\mathrm{\mu }}_M=105 \\ {\mathrm{\sigma }}_M=35 \end{gathered}$$

F=SSHA score of a female student from a large university who was chosen at random.

M=SSHA score of a male student from a large university who was chosen at random.

Calculations

$$\begin{gathered} \mathrm{\mu }={\mathrm{\mu }}_{\mathrm{F}}-{\mathrm{\mu }}_{\mathrm{M}} \\ =120-105 \\ =15 \end{gathered}$$

There are two different random variables with two different means, ${\mathrm{\mu }}_{\mathrm{F}}=120$and${\mathrm{\mu }}_{\mathrm{M}}=105$

as a result, the average of the two random numbers ,the total of their means will be the variable.

On average, there will be a total number of 3.1 errors