Q: A manufacturer claims the mean diameter of bolts is 30mm. You collect a sample and want to test this claim. Which is the correct formulation of the null and alternative hypotheses?

$$H_0$$: \mu = 30$$, H_1$: \mu \neq 30$$

Question 1

Which of the following statements correctly describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

It represents the current belief and is always about a population parameter.

Question 2

A manufacturer claims the mean diameter of bolts is 30mm. You collect a sample and want to test this claim. Which is the correct formulation of the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 30$$, H_1$: \mu 
eq 30$$

Question 3

In hypothesis testing, what does a Type I error represent?

Accepted Answer

Rejecting a true null hypothesis.

Question 4

If the probability of a Type I error ($$\alpha) $$increases, what happens to the probability of a Type II error ($$\beta$$), all else equal?

Accepted Answer

$$\beta$$ decreases

Question 5

Which formula is used to calculate the Z test statistic for a one-sample mean test when the population standard deviation is known?

Accepted Answer

$$Z_{STAT} = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}$$

Question 6

A sample of 100 bolts has a mean diameter of 29.84mm. The population standard deviation is 0.8mm. Test the claim that the true mean is 30mm at $$\alpha = 0.05. $$What is the value of the test statistic?

Accepted Answer

$$Z_{STAT} = -2.0$$

Question 7

In a two-tailed Z test with $$\alpha = 0.05$$, what are the critical values for the test statistic?

Accepted Answer

$$\pm 1.96$$

Question 8

If the calculated test statistic falls in the non-rejection region, what is the correct decision?

Accepted Answer

Do not reject the null hypothesis.

Question 9

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

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than the observed value, given $$H_0 is $$true.

Question 10

A researcher performs a hypothesis test and obtains a p-value of 0.0456 with $$\alpha = 0.05. $$What should the researcher conclude?

Accepted Answer

Reject $$H_0$$ because the p-value is less than $$\alpha.$$

Question 11

Which of the following factors will decrease the probability of a Type II error ($$\beta$$), all else equal?

Accepted Answer

Increasing the level of significance ($$\alpha)$$

Question 12

In the context of hypothesis testing, what does the 'power' of a statistical test refer to?

Accepted Answer

The probability of rejecting $$H_0$$ when it is false.

Question 13

A company wants to test if the mean monthly cell phone bill in a city is $$\mu = 42. $$Which of the following is a correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu 
eq 42$$

Question 14

Which step in the critical value approach to hypothesis testing involves determining the critical values that divide the rejection and nonrejection regions?

Accepted Answer

Step 4

Question 15

In a two-tailed hypothesis test, what is the rejection region for $$\alpha = 0.05$$?

Accepted Answer

$$Z  1.96$$

Question 16

Which of the following is NOT a correct property of the alternative hypothesis ($$H_1$$)?

Accepted Answer

It is always about a sample statistic.

Question 17

A sample mean is very close to the population mean stated in $$H_0. $$What is the most appropriate decision?

Accepted Answer

Do not reject $$H_0$$

Question 18

Which of the following is the correct interpretation of the confidence coefficient ($$1-\alpha$$)?

Accepted Answer

The probability of not rejecting $$H_0$$ when it is true.

Question 19

Which of the following is a correct step in the p-value approach to hypothesis testing?

Accepted Answer

Compute the p-value after collecting the sample data.

Fundamentals of Hypothesis Testing: One-Sample Tests (Chapter 9 Study Notes)

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