Question 1

In the Monty Hall problem, what is the probability of winning the prize if you switch doors after one non-prize door is revealed?

Accepted Answer

$$\frac{2}{3}$$

Question 2

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 3

If the significance level $$\alpha is $$decreased, what happens to the probability of a Type II error ($$\beta$$), assuming all other factors remain constant?

Accepted Answer

$$\beta$$ increases

Question 4

What is the power of a hypothesis test?

Accepted Answer

The probability of rejecting a false null hypothesis

Question 5

Given $$\alpha = 0.05$$ and $$\beta = 0.20$$, what is the power of the test?

Accepted Answer

$$0.80$$

Question 6

In a courtroom analogy for hypothesis testing, what does the null hypothesis ($$H_0) $$represent?

Accepted Answer

The defendant is innocent

Question 7

Which of the following actions will decrease both Type I and Type II error probabilities?

Accepted Answer

Increasing the sample size

Question 8

Suppose you conduct a hypothesis test and fail to reject the null hypothesis when it is actually false. What type of error have you made?

Accepted Answer

Type II error

Question 9

A researcher claims that a new drug is effective. The null hypothesis is that the drug has no effect. If the researcher rejects the null hypothesis when it is actually true, what is the probability of this error called?

Accepted Answer

Type I error ($$\alpha)$$

Question 10

Which formula correctly represents the test statistic for a sample proportion $$p$$ compared to a hypothesized proportion $$p_0$$?

Accepted Answer

$$z = \frac{p - p_0$}{\sqrt{\frac{p_0$(1-p_0$)}{n}}}$$

Question 11

In the context of hypothesis testing, what does the area under the normal curve represent?

Accepted Answer

The total probability, which equals 1

Question 12

A scientist wants to minimize the chance of convicting an innocent person in a hypothesis test. Which error probability should they focus on reducing?

Accepted Answer

Type I error ($$\alpha)$$

Question 13

If the null hypothesis is true and you fail to reject it, what is this outcome called?

Accepted Answer

Correct decision

Question 14

Which of the following statements about $$\alpha$$ and $$\beta is $$true?

Accepted Answer

Increasing $$\alpha$$ decreases $$\beta$$

Question 15

A company tests if a new process increases production. The null hypothesis is that there is no increase. If the company fails to detect a real increase, what error have they made?

Accepted Answer

Type II error

Hypothesis Testing: Proportions, Type I & II Errors, and Power

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