Q: A pharmaceutical company claims that only 2% of children taking their new antibiotic experience headaches as a side effect. A researcher wants to test if the true proportion is different from 2%. Which of the following correctly states the null and alternative hypotheses for this test?

$$H_0$$: p = 0.02$$ and H_1$: p \neq 0.02$$

Q: Which of the following best describes a two-tailed hypothesis test?

The alternative hypothesis uses $$\neq$$ and tests for any difference from the null value.

Q: A researcher is testing whether a new teaching method changes the average test score from 75. Which of the following sets of hypotheses is appropriate for a two-tailed test?

$$H_0$$: \mu = 75$$ and H_1$: \mu \neq 75$$

Question 1

A pharmaceutical company claims that only 2% of children taking their new antibiotic experience headaches as a side effect. A researcher wants to test if the true proportion is different from 2%. Which of the following correctly states the null and alternative hypotheses for this test?

Accepted Answer

$$H_0$$: p = 0.02$$ and H_1$: p 
eq 0.02$$

Question 2

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

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$true

Question 3

A manufacturer wants to know if a new filling machine has less variability than the old one, which has a standard deviation of 0.23 ounces. What are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: \sigma = 0.23$$ and H_1$: \sigma \u003c 0.23$$

Question 4

In the context of hypothesis testing, what does the level of significance $$\alpha$$ represent?

Accepted Answer

The probability of making a Type I error

Question 5

A community college administrator is concerned that the mean time to complete a placement exam is longer than 60 minutes. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003e 60$$

Question 6

If a researcher fails to reject the null hypothesis when the alternative hypothesis is actually true, what type of error has occurred?

Accepted Answer

Type II error

Question 7

Suppose you conduct a hypothesis test and the sample evidence leads you to reject the null hypothesis. What is the correct way to state your conclusion?

Accepted Answer

There is sufficient evidence to support the alternative hypothesis.

Question 8

Which of the following statements about the null hypothesis $$H_0 is $$correct?

Accepted Answer

It always contains a statement of equality.

Question 9

A fair coin is flipped 5 times. What is the probability of getting all tails, assuming the coin is fair?

Accepted Answer

$$\left( \frac{1}{2} \$$right)^5$$ = 0.03125$$

Question 10

Which of the following best describes a two-tailed hypothesis test?

Accepted Answer

The alternative hypothesis uses $$
eq$$ and tests for any difference from the null value.

Question 11

If the probability of making a Type I error increases, what happens to the probability of making a Type II error, all else being equal?

Accepted Answer

It decreases.

Question 12

Which of the following is NOT a correct step in the process of hypothesis testing?

Accepted Answer

Accept the null hypothesis if the evidence is weak.

Question 13

A researcher is testing whether a new teaching method changes the average test score from 75. Which of the following sets of hypotheses is appropriate for a two-tailed test?

Accepted Answer

$$H_0$$: \mu = 75$$ and H_1$: \mu 
eq 75$$

Question 14

In a hypothesis test, which of the following is the correct definition of $$\beta$$?

Accepted Answer

$$\beta = P(	ext{Type II error}) = P(	ext{not rejecting } H_0$ 	ext{ when } H_1$ 	ext{ is true})$$

Question 15

A company is testing whether a new process reduces the mean production time below 10 hours. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c 10$$

Question 16

Which of the following real-world scenarios best illustrates a Type II error?

Accepted Answer

A medical test fails to detect a disease when the patient actually has it.

Question 17

In hypothesis testing, why do we say 'do not reject the null hypothesis' instead of 'accept the null hypothesis'?

Accepted Answer

Because we do not have access to the entire population and cannot know the exact parameter value.

Question 18

A researcher is testing $$H_0$$: \mu = 100$$ vs H_1$: \mu \u003e 100. $$What type of test is this?

Accepted Answer

Right-tailed test

Question 19

Which of the following is a correct interpretation of 'rejecting the null hypothesis' in a real-world context?

Accepted Answer

There is sufficient evidence to conclude that the effect or difference exists.

Hypothesis Testing: The Language and Logic of Statistical Inference

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