The same researcher wants to see if recently widowed spouses leave the house more after they perform some activity (e. g., Bingo, Support Group, etc.). She wants to compare participants before and after a group activity. Which type of t-test should she use?

paired t-test

Step-by-step explanation:

Paired t-test is used to measure before and after effect. For example, a researcher wants to check the effect of new teaching method and he wants to compares marks of students before new teaching method and marks of students before new teaching method.

In the given example there are two groups participants before group activity and participants after group activity. A researcher wants to investigate that whether recently widowed spouses leave house after performing group activity or not. The observations in these two groups are paired naturally and we take the differences of these two groups are considered as random sample. This type of t-test is known as paired t-test.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.