Question 1

Which of the following best describes the null hypothesis ($$H_0) in a $$hypothesis test?

Accepted Answer

A statement that is assumed true unless there is strong evidence against it.

Question 2

A researcher claims that the average pollution level in a river is different from 2.5 mg/L. A sample of 72 measurements yields a mean of 2.37 mg/L and a standard deviation of 1.21 mg/L. What is the value of the test statistic for this hypothesis test?

Accepted Answer

$$z = \dfrac{2.37 - 2.5}{1.21 / \sqrt{72}} = -0.91$$

Question 3

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

Accepted Answer

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

Question 4

Which formula is used to calculate the test statistic for a large sample hypothesis test for a population mean?

Accepted Answer

$$z = \dfrac{\bar{x} - \mu}{s / \sqrt{n}}$$

Question 5

A production line is supposed to fill containers with 500 grams of product. A sample of 20 containers has a mean of 510 grams and a standard deviation of 25 grams. What is the value of the test statistic for testing if the machine is overfilling or underfilling?

Accepted Answer

$$t = \dfrac{510 - 500}{25 / \sqrt{20}} = 1.78$$

Question 6

Which of the following statements about the significance level ($$\alpha) is $$correct?

Accepted Answer

It is the probability of rejecting $$H_0$$ when $$H_0 is $$true.

Question 7

Which test should be used when testing a hypothesis about a population mean with a sample size less than 30 and the population is approximately normally distributed?

Accepted Answer

A t-test using the t-distribution.

Question 8

In a two-tailed hypothesis test at the 5% significance level, what are the critical values for the z-test?

Accepted Answer

$$-1.96$$ and $$1.96$$

Question 9

A Type II error in hypothesis testing is best described as:

Accepted Answer

Failing to reject $$H_0$$ when $$H_0 is $$false.

Question 10

Which of the following changes will increase the power of a hypothesis test?

Accepted Answer

Increasing the sample size.

Question 11

A hospital administrator wants to test if the average waiting time in the emergency room is less than 30 minutes. Which is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu \geq 30$$, H_a$$: \mu \u003c 30$$

Question 12

Which of the following is NOT a step in conducting a hypothesis test for a population mean (large sample)?

Accepted Answer

Calculate the population mean from the sample.

Question 13

A two-tailed test is always valid because:

Accepted Answer

It tests for deviations in both directions from the hypothesized mean.

Question 14

If the test statistic falls within the critical region, what is the correct decision?

Accepted Answer

Reject $$H_0.$$

Question 15

Which of the following best describes the alternative hypothesis ($$H_a$$)?

Accepted Answer

It is accepted if there is enough evidence to reject $$H_0.$$

Question 16

In a small sample hypothesis test ($$n \u003c 30$$), which distribution is used to determine the critical value?

Accepted Answer

t-distribution with $$n-1$$ degrees of freedom

L 11 Hypothesis Testing for One Population Mean: Large and Small Samples

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