A researcher in a Human Resources Unit presented a recent study, which showed a statistical significance between length of staff lunch breaks and low productivity; how can she explain to her manager that this does not mean that the length of staff lunch breaks should be reduced?

1. A significant result means that the effect is strong.
2. A significant result means that the effect is not relevant.
3. A significant result does not mean that the effect is important.
4. A significant result means that the effect is weak.

To explain to her manager that her research does not mean the length of staff lunch breaks should be reduced, the best thing to say from the options is:

A significant result does not mean that the effect is important.

Step-by-step explanation:

1. Saying "A significant result means that the effect is strong.", she is contradicting the message she is trying to pass across, as this would only trigger her manager to reduce the length of lunch break. The manager would take very seriously anything that has a strong effect on their productivity.

2. Saying "A significant result means that the effect is not relevant" wouldn't pass her intended message across. The effect might not be relevant to productivity, but will be relevant to another department, so something would be done about their lunch time break.

3. Saying "A significant result does not mean that the effect is important", she would pass her message very clearly. The manager would hear of a negligible effect, and would not worry about any effect of their lunch break time.

4. Saying "A significant result means that the effect is weak", she sounds direct, admitting that there is an effect, but a weak one. That is not good enough.

The measure of angle A is 59 degrees.

When you have a quadrilateral inscribed in a circle the opposite sides are always supplementary (add to 180). Given the order of the vertices of our quadrilateral, we know that A and C are opposite.

Therefore, we can write and solve the following equation.
A + C = 180
A + 121 = 180
A = 59 degrees