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 2

The experiment is properly randomized as the friend randomly assigns the position of the correct picture on each trial

step 3

Next, we check the condition $np \geq 10$ and $n(1-p) \geq 10$ using the given sample size $n=60$ and the probability under the null hypothesis $p=0.25$

step 4

Calculate $np$ using the asksia-ll calculation: $60 \times 0.25 = 15$

step 5

Calculate $n(1-p)$ using the asksia-ll calculation: $60 \times (1-0.25) = 45$

step 6

Since both $np = 15$ and $n(1-p) = 45$ are greater than 10, the condition is met

step 7

Lastly, we consider if each trial can be considered independent

step 8

Since the position of the correct picture is randomly assigned each time and there are only 60 trials, it is reasonable to assume that each trial is independent

1 Answer

A, B, C

Key Concept

Conditions for Significance Testing

Explanation

In hypothesis testing, it is important to ensure that the experiment is properly randomized, that the sample size is large enough to satisfy $np \geq 10$ and $n(1-p) \geq 10$, and that each trial is independent. These conditions help validate the use of certain statistical tests and the reliability of the results.

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