8.2 Z test for a Mean

Multiple Choice

Scenario:

An energy drink company claims that their drink provides an average of 120 mg of caffeine per can.

A group of students suspects:

“The drink actually contains more than 120 mg of caffeine.”

Write:

•Null hypothesis (H₀): ______

•Alternative hypothesis (H₁): ______

• H₀: The average caffeine content is 120 mg. H₁: The average caffeine content is greater than 120 mg.
• H₀: The average caffeine content is less than 120 mg.
• H₁: The average caffeine content is equal to 120 mg.
• H₀: The average caffeine content is exactly 100 mg.

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Open Ended

Describe the process of comparing the z-score to the critical value and making a decision in hypothesis testing, as illustrated in the Explore Activity and Answer Key.

Multiple Choice

Which of the following are required to calculate the z test statistic for a mean?

• Sample mean, hypothesized population mean, population standard deviation, sample size

• Sample mean, sample standard deviation, population mean, sample size

• Sample mean, population mean, sample size

• Sample mean, hypothesized population mean, sample size

Open Ended

Compare the decision-making process in Example 1 and Example 2. What determines whether the null hypothesis is rejected or not in each case?

Multiple Choice

Which of the following statements best describes the result of Example 3 regarding the average number of times a person skips breakfast per year?

• There is enough evidence to support the claim that the mean is not equal to 50.

• There is not enough evidence to support the claim that the mean is not equal to 50.

• The mean is exactly 50.

• The mean is less than 50.

Multiple Select

Select all correct guidelines for interpreting P-values according to the table shown.

• P-value ≤ 0.01: Reject the null hypothesis. The difference is highly significant.

• 0.01 < P-value ≤ 0.05: Reject the null hypothesis. The difference is significant.

• 0.05 < P-value ≤ 0.10: Consider the consequences of type I error before rejecting the null hypothesis.

• P-value > 0.10: Do not reject the null hypothesis. The difference is not significant.

Open Ended

In Example 4, explain how the P-value method is used to determine whether the average cost of tuition and fees at four-year public colleges is greater than $5700.

Multiple Choice

Which step in the z test for a mean–not equal involves calculating the test statistic, and what formula is used for this calculation?

• Step 1: State the hypotheses

• Step 2: Compute the test statistic, using z = (X̄ - μ) / (σ / √n)

• Step 3: Find the P-value

• Step 4: Make the decision

Open Ended

Compare the hypothesis testing examples for wind speed (Image 0) and luxury watch cost (Image 1). What is the key difference in the final decision for each scenario?

Multiple Select

Based on the hypothesis testing scenarios in Images 2 and 3, select all situations where the null hypothesis is NOT rejected.

• Average temperature differs from 29°F (Image 2)

• Mean number of cell phone calls is greater than 2.8 (Image 3)

• Mean cost of luxury watch is less than $7521 (Image 1)

• Average wind speed is not equal to 8 mph (Image 0)

Multiple Choice

Which of the following is NOT a step in the traditional hypothesis testing process as outlined in the images?

• State the hypotheses and identify the claim

• Find the critical value(s) or use the P-value method

• Compute the test statistic

• Draw a histogram of the data

Open Ended

Explain how the significance level α and the P-value are used together to make a decision in hypothesis testing. Provide an example from the images to support your explanation.

Multiple Choice

Which of the following is a key objective when applying the Z test for a mean using the traditional method?

• To make decisions about population claims

• To calculate the median of a data set

• To determine the mode of a distribution

• To find the range of a sample

Open Ended

What questions do you still have about statistics or the resources used in today's lesson?

Multiple Choice

Reflecting on today's statistics lesson, what resource did you find most helpful for your learning experience?

• Book

• Calculator

• Notebook Heading

• Clean & Organized Classroom