Q: A pharmaceutical company claims that the proportion of children experiencing headaches as a side effect from a new antibiotic is different from the 2% observed with competing antibiotics. Which of the following correctly states the null and alternative hypotheses for this scenario?

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

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

$$\alpha = P(\text{Type I error})$$

Q: A researcher wants to test if the mean length of a phone call has increased from the previously reported 3.25 minutes. Which of the following is the correct set of hypotheses?

$$H_0$$: \mu = 3.25$$ \newline H_1$: \mu \u003e 3.25$$

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

The alternative hypothesis contains a $$\neq$$ symbol

Question 1

A pharmaceutical company claims that the proportion of children experiencing headaches as a side effect from a new antibiotic is different from the 2% observed with competing antibiotics. Which of the following correctly states the null and alternative hypotheses for this scenario?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Suppose a new filling machine is being tested to see if it reduces the standard deviation of detergent in bottles from the current value of 0.23 ounces. What is the correct null hypothesis?

Accepted Answer

$$H_0$$: \sigma = 0.23$$

Question 5

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

Accepted Answer

$$\alpha = P(	ext{Type I error})$$

Question 6

A researcher wants to test if the mean length of a phone call has increased from the previously reported 3.25 minutes. Which of the following is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu = 3.25$$ 
ewline H_1$: \mu \u003e 3.25$$

Question 7

Which of the following statements is TRUE regarding the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

It always contains a statement of equality

Question 8

If a hypothesis test results in not rejecting the null hypothesis, which of the following is the most appropriate conclusion?

Accepted Answer

There is not sufficient evidence to support the alternative hypothesis

Question 9

A researcher sets $$\alpha = 0.05$$ for a hypothesis test. What does this mean in the context of the test?

Accepted Answer

There is a 5% probability of rejecting $$H_0$$ when $$H_0 is $$actually true

Question 10

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

Accepted Answer

The alternative hypothesis contains a $$
eq$$ symbol

Question 11

In a hypothesis test, which of the following outcomes is a Type II error?

Accepted Answer

Failing to reject $$H_0$$ when $$H_1 is $$true

Question 12

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

Accepted Answer

$$0.03125$$

Question 13

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

Accepted Answer

Accept the null hypothesis if the evidence is weak

Question 14

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

Accepted Answer

It decreases

Question 15

A quality control manager wants to test if a new process has decreased the standard deviation of wine in bottles from 0.23 ounces. What is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \sigma \u003c 0.23$$

Question 16

Which of the following real-world scenarios would most likely require a left-tailed hypothesis test?

Accepted Answer

Testing if a new machine has less variability than the old one

Question 17

Why do we say 'do not reject the null hypothesis' instead of 'accept the null hypothesis'?

Accepted Answer

Because we do not know the exact value of the parameter without access to the entire population

Question 18

Which of the following is the correct symbolic representation for a right-tailed test about a population mean?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$ 
ewline $$H_1$$: \mu \u003e \$$mu_0$$

Question 19

A researcher fails to reject the null hypothesis that the proportion of children experiencing a headache is 0.02, when in fact it is different. What type of error has occurred?

Accepted Answer

Type II error

Hypothesis Tests Regarding a Parameter: Structured Study Notes

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