Question

Math

Posted 6 months ago

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Alden claims he is psychic. His friend designs a game to test his psychic abilities. The friend will present Alden with four different cards and ask him to identify which card has a certain picture on it. Only one card has the correct picture, and the friend will randomly assign the position of the correct picture on each trial. So they're willing to assume that Alden has a $25 \%$ chance of guessing correctly on any given trial.
They plan to carry out 60 trials of this experiment to test $H_{0}: p=0.25$ versus $H_{\mathrm{a}}: p>0.25$, where $p$ is the proportion of trials that Alden would identify the correct card.
Which conditions for performing this type of significance test have been met?
Choose all answers that apply:
A They properly randomized the experiment.
B $n p \geq 10$ and $n(1-p) \geq 10$
c Each trial can be considered independent.
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

Evaluate the condition for randomization

step 2

The experiment is properly randomized as each card's position is assigned randomly for each trial

step 3

Check the sample size condition using the Asksia-LL calculator result for $np \geq 10$ and $n(1-p) \geq 10$

step 4

Using the given proportion $p=0.25$ and sample size $n=60$, calculate $np$ and $n(1-p)$

step 5

For $np$: $60 \times 0.25 \geq 10$ is True according to Asksia-LL calculator

step 6

For $n(1-p)$: $60 \times (1-0.25) \geq 10$ is also True according to Asksia-LL calculator

step 7

Evaluate the independence condition

step 8

Each trial can be considered independent because the outcome of one trial does not affect the outcome of another

[question number] Answer

A, B, and C conditions have been met for performing this type of significance test.

Key Concept

Conditions for a significance test

Explanation

In hypothesis testing, proper randomization ensures that the sample represents the population, the sample size condition ensures that the normal approximation is valid, and the independence condition ensures that the trials do not influence each other.

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