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### 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 $20\mathrm{%}$ 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 $20\mathrm{%}$ 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 $10$?
$\phantom{\rule{2em}{0ex}}$
Let's agree that if the observed outcome has a probability less than $1\mathrm{%}$ under the tested hypothesis, we will reject the hypothesis.
What should we conclude regarding the hypothesis?
$\mathrm{#}$ of "Ask again later" out of $10$Frequency
$0$$107$
$1$$268$
$2$$303$
$3$$201$
$4$$88$
$5$$26$
$6$$6$
$7$$1$
$8$$0$
$9$$0$
$10$$0$