Q: A researcher wants to show that a new teaching method changes the average test score from 75. What are the null and alternative hypotheses?

$$H_0$$: \mu = 75$$ H_a$$: \mu \neq 75$$

Question 1

A pharmaceutical company claims that its new drug reduces the average recovery time from the flu to less than 5 days. Which of the following correctly states the null and alternative hypotheses for a hypothesis test to support the company's claim?

Accepted Answer

$$H_0$$: \mu \geq 5$$ 
H_a$$: \mu \u003c 5$$

Question 2

A school claims that at least 70% of its students participate in extracurricular activities. Which of the following is the correct alternative hypothesis for testing if the actual proportion is less than claimed?

Accepted Answer

$$H_a: p \u003c 0.70$$

Question 3

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

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 4

A meat inspector tests whether the proportion of contaminated beef exceeds the USDA limit of 7.5%. If the actual contamination is below the limit but the inspector concludes it is above, what type of error has occurred?

Accepted Answer

Type I error

Question 5

If the level of significance $$\alpha is $$set to 0.01, what does this mean in the context of hypothesis testing?

Accepted Answer

There is a 1% maximum probability of making a Type I error.

Question 6

Which of the following scenarios requires a two-tailed hypothesis test?

Accepted Answer

Testing if the mean weight of a product is different from 100 grams.

Question 7

A researcher wants to show that a new teaching method changes the average test score from 75. What are the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 75$$ 
H_a$$: \mu 
eq 75$$

Question 8

Which of the following is the correct interpretation if you fail to reject the null hypothesis in a hypothesis test?

Accepted Answer

There is not enough evidence to support the alternative hypothesis.

Question 9

A car dealership claims the mean oil change time is less than 15 minutes. You perform a hypothesis test and reject $$H_0$$: \mu \geq 15$$. What is the correct conclusion?

Accepted Answer

There is enough evidence to support the dealership's claim.

Question 10

Which of the following best describes the P-value in hypothesis testing?

Accepted Answer

The probability, assuming $$H_0 is $$true, of obtaining a result as extreme or more extreme than the observed statistic.

Question 11

A company advertises that the mean life of its furnaces is more than 18 years. Which type of test should be used to evaluate this claim?

Accepted Answer

Right-tailed test

Question 12

Which of the following is a correct decision rule based on the P-value?

Accepted Answer

Reject $$H_0 if$$ $$P-$$value $$\leq \alpha$$

Question 13

Which of the following is an example of a null hypothesis?

Accepted Answer

$$H_0$$: p = 0.5$$

Question 14

If a Type II error occurs in a medical test for a disease, what is the consequence?

Accepted Answer

A sick patient is incorrectly told they are healthy.

Question 15

Which symbol is commonly used to denote the level of significance in hypothesis testing?

Accepted Answer

$$\alpha$$

Question 16

A researcher wants to test if the average commute time is not equal to 30 minutes. What is the correct form of the alternative hypothesis?

Accepted Answer

$$H_a: \mu 
eq 30$$

Question 17

Which of the following is NOT a possible outcome of a hypothesis test?

Accepted Answer

Accept the alternative hypothesis

Question 18

In a left-tailed test, which inequality symbol is used in the alternative hypothesis?

Accepted Answer

\u003c

Question 19

Which of the following best describes the relationship between the null and alternative hypotheses?

Accepted Answer

They are complementary; if one is false, the other must be true.

Question 20

A hypothesis test is performed at $$\alpha = 0.05$$ and the P-value is 0.03. What is the correct decision?

Accepted Answer

Reject the null hypothesis.

Section 7.1: Introduction to Hypothesis Testing – Structured Study Notes

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