Question 1

Which of the following is NOT a condition that must be satisfied before testing a hypothesis regarding a population mean $$\mu$$?

Accepted Answer

The population standard deviation $$\sigma$$ must be known.

Question 2

A researcher wants to test if the mean debt payment in Wyoming is less than the national mean of $$\24$$,254$. Which of the following is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu = 24,254$$

Question 3

Which test should be used to determine if a sample is drawn from a population that is normally distributed?

Accepted Answer

A normality test such as the Shapiro-Wilk test

Question 4

When testing a hypothesis about a population mean with a small sample size ($$n \u003c 30) $$and unknown population standard deviation, which test statistic should be used?

Accepted Answer

The t-statistic: $$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$$

Question 5

Which of the following best describes the difference between statistical significance and practical significance?

Accepted Answer

Statistical significance refers to the likelihood that a result is not due to random variation, while practical significance refers to whether the result is large enough to be meaningful in context.

Question 6

A manufacturer claims that the mean weight of their 'fun size' bars is 20 grams. A sample of 8 bars has a mean of 19.6 grams and a standard deviation of 0.5 grams. What is the value of the test statistic for testing $$H_0$$: \mu = 20$$ at $$\alpha = 0.05$$?

Accepted Answer

$$t = \frac{19.6 - 20}{0.5 / \sqrt{8}} = -2.26$$

Question 7

Which of the following is the correct sequence of steps for testing a hypothesis about a population mean?

Accepted Answer

State the hypotheses, collect data, calculate the test statistic, make a decision, interpret the result.

Question 8

If a sample contains outliers, which of the following is the most appropriate action before conducting a hypothesis test about the mean?

Accepted Answer

Investigate the cause of the outliers and consider using a robust statistical method or transforming the data.

Question 9

A large sample size can lead to which of the following issues when interpreting statistical significance?

Accepted Answer

It can make small, trivial differences appear statistically significant.

Question 10

In the context of hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of obtaining a result as extreme as the observed one, assuming the null hypothesis is true.

Question 11

A city claims that the mean travel time to work is 27.8 minutes. A new survey finds a mean of 27.3 minutes with a large sample size and a statistically significant result at $$\alpha = 0.01. $$What should be considered before concluding that travel times have meaningfully decreased?

Accepted Answer

Whether the difference of 0.5 minutes is practically significant.

Question 12

Which of the following is a correct interpretation if the p-value is less than the significance level $$\alpha$$?

Accepted Answer

Reject the null hypothesis.

Question 13

A sample of 30 individuals with a bachelor's degree in Wyoming has a mean debt payment of $$\14$$,014$$ and a standard deviation of $$\$$1,500. $$The national mean is $$\24$$,254$$. What is the value of the z-statistic for testing H_0$: \mu = 24,254$?

Accepted Answer

$$z = \frac{14,014 - 24,254}{1,500 / \sqrt{30}} = -37.5$$

Question 14

Which of the following is NOT a step in the hypothesis testing procedure for a population mean?

Accepted Answer

Estimate the population proportion.

Question 15

A student tests whether the mean weight of a product is different from the advertised mean using a sample of 8 measurements. The sample mean is 21.2g, the sample standard deviation is 0.6g, and the advertised mean is 21g. What is the value of the t-statistic?

Accepted Answer

$$t = \frac{21.2 - 21}{0.6 / \sqrt{8}} = 0.94$$

Question 16

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

Accepted Answer

Rejecting a true null hypothesis.

Question 17

If the sample size is small and the population is not normally distributed, which of the following is the most appropriate action?

Accepted Answer

Use a nonparametric test such as the Wilcoxon signed-rank test.

Question 18

Which of the following is a reason to use technology (such as statistical software) when performing hypothesis tests?

Accepted Answer

To handle large datasets and complex calculations efficiently.

Question 19

A researcher finds a statistically significant difference between two means, but the difference is only 0.1 units. What should the researcher consider before making recommendations?

Accepted Answer

Whether the difference is practically significant.

Section 10.3 Hypothesis Tests for a Population Mean: Concepts, Steps, and Applications

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