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Flashcards: Statistics

Type II errors occur when a researcher incorrectly __________ the ___________ hypothesis; therefore, they erroneously reject the __________ hypothesis.

accepts. . . null. . . alternative

rejects. . . null. . . alternative

rejects. . . alternative. . . null

accepts. . . alternative. . . null

None of these

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Flashcards: Statistics

Type II errors occur when a researcher incorrectly __________ the ___________ hypothesis; therefore, they erroneously reject the __________ hypothesis.

Your answer:

rejects. . . null. . . alternative

Your answer:

rejects. . . alternative. . . null

Your answer:

accepts. . . alternative. . . null

Your answer:

None of these

Correct answer:

accepts. . . null. . . alternative

Explanation:

Type II errors occur when we fail to reject a false null hypothesis. As a result, the researcher will incorrectly accept the null hypothesis and erroneously reject the alternative hypothesis. This commonly occurs when sample sizes are small. Larger sample sizes ensure that statistical measures will identify a practical difference when one truly exists.

Flashcards: Statistics

What is the probability of rolling "snake eyes"—a value of one on two separate dice—using two fair dice?

$\frac{1}{12}$

$\frac{1}{7}$

$\frac{1}{49}$

$\frac{1}{6}$

$\frac{1}{36}$

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Flashcards: Statistics

What is the probability of rolling "snake eyes"—a value of one on two separate dice—using two fair dice?

Your answer:

$\frac{1}{12}$

Your answer:

$\frac{1}{7}$

Your answer:

$\frac{1}{49}$

Your answer:

$\frac{1}{6}$

Correct answer:

$\frac{1}{36}$

Explanation:

In order to solve this standard, we need to understand two primary components: probabilities and the property of independent events. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

$P=\frac{\textup{event: particular phenomenon we wish to observe}}{\textup{sample space: total number of possible outcomes}}$

Let's use this information to solve our problem. First, let's calculate the probability of rolling a one. There is a single side of the die that has a value of one and there are six total sides on the die; therefore, we can write the following formula:

$P(rolling \ one\ on\ the\ first\ die)=\frac{\textup{event: particular phenomenon we wish to observe}}{\textup{sample space: total number of possible outcomes}}$

$P(rolling \ one\ on\ the\ first\ die)=\frac{1}{6}$

Now, let's find the probability of rolling a two on a separate die in the same roll.

$P(rolling \ one\ on\ the\ second\ die)=\frac{\textup{event: particular phenomenon we wish to observe}}{\textup{sample space: total number of possible outcomes}}$

$P(rolling \ one\ on\ the\ second\ die)=\frac{1}{6}$

Last, we need multiply these two probabilities together.

$P(snake\ eyes)=P(rolling\ one\ on\ the\ first\ die) \times P(rolling\ one\ on\ the\ second\ die)$

$P(snake\ eyes)=\frac{1}{6}\times \frac{1}{6}$

$P(snake\ eyes)=\frac{1}{36}$

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Flashcards: Statistics

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Flashcards: Statistics

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Complaint Details

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