Question 1

Which of the following best describes the purpose of inferential statistics?

Accepted Answer

To use probability theory to relate descriptive statistics of the sample to make statements about the population.

Question 2

A researcher wants to test if the mean weight of a certain brand of tyres is 56 kg. Which is the correct null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: \mu = 56$$

Question 3

Which of the following statements about the alternative hypothesis ($$H_1) is $$TRUE?

Accepted Answer

It is the hypothesis the researcher wishes to support.

Question 4

If a hypothesis test is conducted at a significance level $$\alpha = 0.05$$, what does this mean?

Accepted Answer

There is a 5% chance of rejecting the null hypothesis when it is actually true.

Question 5

Which of the following is an example of a Type I error in a medical diagnostic test?

Accepted Answer

Incorrectly concluding that a healthy patient has the disease.

Question 6

Given the formula for a confidence interval for the mean when population standard deviation is known: $$\bar{X} \pm Z \frac{\sigma}{\sqrt{n}}$$, what does $$Z$$ represent?

Accepted Answer

The critical value from the standard normal distribution

Question 7

A company wants to test if more than 10% of its products are defective. Which is the correct alternative hypothesis ($$H_1$$)?

Accepted Answer

$$H_1$$: p \u003e 0.10$$

Question 8

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

Accepted Answer

The alternative hypothesis is non-directional, such as $$H_1$$: \mu 
eq \$$mu_0.$$

Question 9

Suppose a sample of 100 students has a mean test score of 75 and a population standard deviation of 10. What is the $$Z-$$statistic for testing if the population mean is 72?

Accepted Answer

$$Z = \frac{75 - 72}{10/\sqrt{100}} = 3$$

Question 10

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

Accepted Answer

Calculate the population parameter

Question 11

A researcher sets $$\alpha = 0.01$$ for a hypothesis test. What is the main consequence of this choice?

Accepted Answer

It decreases the probability of making a Type I error.

Question 12

In a two-sample $$Z-$$test for the difference of means, which formula is used for the standard error if both samples are independent?

Accepted Answer

$$\sqrt{\frac{\$$sigma_1$$^2}{n_1$} + \frac{\$$sigma_2$$^2}{n_2$}}$$

Question 13

A sample of 172 credit card balances has a mean of $$407 and a sample standard deviation of 38. If $$the population mean is hypothesized to be $$400, what is the Z$-statistic?

Accepted Answer

$$Z = \frac{407 - 400}{38/\sqrt{172}} \approx 2.42$$

Question 14

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

Accepted Answer

A person with a disease is incorrectly told they are healthy.

Question 15

If the critical value for a one-tailed $$Z-$$test at $$\alpha = 0.05 is 1.645$$, what should you conclude if your calculated $$Z-$$statistic is 2.10?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following is TRUE about the decision rule in hypothesis testing?

Accepted Answer

It is based on the critical value and level of significance.

Question 17

A two-tailed test at $$\alpha = 0.05$$ has what critical $$Z-$$values?

Accepted Answer

$$\pm 1.96$$

Question 18

Which of the following is a correct interpretation of 'failing to reject the null hypothesis'?

Accepted Answer

There is not enough evidence to support the alternative hypothesis.

Hypothesis Testing: Concepts, Steps, and Applications

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