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## Statistics and probability

### Course: Statistics and probability>Unit 12

Lesson 1: The idea of significance tests

# Simple hypothesis testing

You might need: Calculator

## Problem

Niels has a Magic 8-Ball, which is a toy used for fortune-telling or seeking advice. To consult the ball, you ask the ball a question and shake it. One of 5 different possible answers then appears at random in the ball. Niels sensed that the ball answers "Ask again later" too frequently. He used the ball 10 times and got "Ask again later" 6 times.
Let's test the hypothesis that each answer has an equal chance of 20, percent of appearing in the Magic 8-Ball versus the alternative that "Ask again later" has a greater probability.
The table below sums up the results of 1000 simulations, each simulating 10 random answers with a 20, percent chance of getting "Ask again later".
According to the simulations, what is the probability of getting "Ask again later" 6 times or more out of 10?
$\qquad$
Let's agree that if the observed outcome has a probability less than 1, percent under the tested hypothesis, we will reject the hypothesis.
What should we conclude regarding the hypothesis?
\# of "Ask again later" out of 10Frequency
0107
1268
2303
3201
488
526
66
71
80
90
100
Stuck?
Stuck?