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the mean caffeine content per 12-ounce bottle of cola is 35 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola company that nas a mean caffeine content of 33.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.4 milligrams. At a=0.01, can you reject the company's daim? Complete parts (a) through Cola dri e). O A. OB. OC. Fail to reject Ho Fail to reject Ho Fail to reject Hg Reject Ho- Reject Ho Reject Ho- Reject Hg by (c) Find the standardized test statistic. z= (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O A. Since z is in the rejection region, fail to reject the null hypothesis. O B. Since z is in the rejection region, reject the null hypothesis. O C. Since z is not in the rejection region, fail to reject the null hypothesis. O D. Since z is not in the rejection region, reject the null hypothesis. Next 11:11 P

the mean caffeine content per 12-ounce bottle of cola is 35 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola company that nas a mean caffeine content of 33.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.4 milligrams. At a=0.01, can you reject the company's daim? Complete parts (a) through Cola dri e). O A. OB. OC. Fail to reject Ho Fail to reject Ho Fail to reject Hg Reject Ho- Reject Ho Reject Ho- Reject Hg by (c) Find the standardized test statistic. z= (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O A. Since z is in the rejection region, fail to reject the null hypothesis. O B. Since z is in the rejection region, reject the null hypothesis. O C. Since z is not in the rejection region, fail to reject the null hypothesis. O D. Since z is not in the rejection region, reject the null hypothesis. Next 11:11 P

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Transcription of Image for Educational Website:** --- A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 35 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 33.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.4 milligrams. At \(\alpha = 0.01\), can you reject the company's claim? Complete parts (a) through (e). **(c) Find the standardized test statistic.** \[ z = \_\_ \text{ (Round to two decimal places as needed.)} \] **(d) Decide whether to reject or fail to reject the null hypothesis.** - **A.** Since \( z \) is in the rejection region, fail to reject the null hypothesis. - **B.** Since \( z \) is in the rejection region, reject the null hypothesis. - **C.** Since \( z \) is not in the rejection region, fail to reject the null hypothesis. - **D.** Since \( z \) is not in the rejection region, reject the null hypothesis. **Graph Details:** There are three diagrams labeled A, B, and C. Each diagram is a bell-shaped curve representing the normal distribution of data: - **Diagram A:** The curve is shaded to indicate the areas where you would reject \( H_0 \) on both tails (two-tailed test). The critical region is marked beyond \( z \) values of approximately \(-2\) and \(2\). - **Diagram B:** The curve indicates rejection of \( H_0 \) on the right tail only (one-tailed test). The rejection region is beyond \( z = 2\). - **Diagram C:** The curve is similar to A, with rejection regions on both sides of the mean, indicating a two-tailed test as well. Each graph is annotated with “Fail to reject \( H_0 \)” and “Reject \( H_0 \)” zones. ---
Transcribed Image Text:**Transcription of Image for Educational Website:** --- A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 35 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 33.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.4 milligrams. At \(\alpha = 0.01\), can you reject the company's claim? Complete parts (a) through (e). **(c) Find the standardized test statistic.** \[ z = \_\_ \text{ (Round to two decimal places as needed.)} \] **(d) Decide whether to reject or fail to reject the null hypothesis.** - **A.** Since \( z \) is in the rejection region, fail to reject the null hypothesis. - **B.** Since \( z \) is in the rejection region, reject the null hypothesis. - **C.** Since \( z \) is not in the rejection region, fail to reject the null hypothesis. - **D.** Since \( z \) is not in the rejection region, reject the null hypothesis. **Graph Details:** There are three diagrams labeled A, B, and C. Each diagram is a bell-shaped curve representing the normal distribution of data: - **Diagram A:** The curve is shaded to indicate the areas where you would reject \( H_0 \) on both tails (two-tailed test). The critical region is marked beyond \( z \) values of approximately \(-2\) and \(2\). - **Diagram B:** The curve indicates rejection of \( H_0 \) on the right tail only (one-tailed test). The rejection region is beyond \( z = 2\). - **Diagram C:** The curve is similar to A, with rejection regions on both sides of the mean, indicating a two-tailed test as well. Each graph is annotated with “Fail to reject \( H_0 \)” and “Reject \( H_0 \)” zones. ---
**Hypothesis Testing Example: Caffeine Content in Cola** **Background:** A cola company claims that the mean caffeine content per 12-ounce bottle of their cola is 35 milligrams. To test this claim, a sample of thirty 12-ounce bottles is analyzed, revealing a mean caffeine content of 33.4 milligrams. The population is assumed to be normally distributed with a population standard deviation of 6.4 milligrams. At a significance level (\(\alpha\)) of 0.01, can the company's claim be rejected? **Tasks:** Complete parts (a) through (c). **(a) Identify \(H_0\) and \(H_a\): Choose the correct answer below.** - Option A: - \(H_0: \mu = 35\) - \(H_a: \mu \neq 35\) - Option B: - \(H_0: \mu = 33.4\) - \(H_a: \mu \neq 33.4\) - Option C: - \(H_0: \mu \leq 33.4\) - \(H_a: \mu > 33.4\) - Option D: - \(H_0: \mu \geq 35\) - \(H_a: \mu < 35\) - Option E: - \(H_0: \mu = 33.4\) - \(H_a: \mu \neq 33.4\) - Option F: - \(H_0: \mu \neq 33.4\) - \(H_a: \mu = 33.4\) **(b) Find the critical value(s):** Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) - Option A: - The critical value is \(\_\_\_\_\_\_\_\_\) - Option B: - The critical values are \(\pm \_\_\_\_\_\_\_\_\) **Identify the rejection region(s):** Choose the correct answer below. - Option A: - Fail to reject \(H_0\). - Option B: - Fail to reject \(H_a\). - Option C: - Fail to reject \(H_1\).
Transcribed Image Text:**Hypothesis Testing Example: Caffeine Content in Cola** **Background:** A cola company claims that the mean caffeine content per 12-ounce bottle of their cola is 35 milligrams. To test this claim, a sample of thirty 12-ounce bottles is analyzed, revealing a mean caffeine content of 33.4 milligrams. The population is assumed to be normally distributed with a population standard deviation of 6.4 milligrams. At a significance level (\(\alpha\)) of 0.01, can the company's claim be rejected? **Tasks:** Complete parts (a) through (c). **(a) Identify \(H_0\) and \(H_a\): Choose the correct answer below.** - Option A: - \(H_0: \mu = 35\) - \(H_a: \mu \neq 35\) - Option B: - \(H_0: \mu = 33.4\) - \(H_a: \mu \neq 33.4\) - Option C: - \(H_0: \mu \leq 33.4\) - \(H_a: \mu > 33.4\) - Option D: - \(H_0: \mu \geq 35\) - \(H_a: \mu < 35\) - Option E: - \(H_0: \mu = 33.4\) - \(H_a: \mu \neq 33.4\) - Option F: - \(H_0: \mu \neq 33.4\) - \(H_a: \mu = 33.4\) **(b) Find the critical value(s):** Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) - Option A: - The critical value is \(\_\_\_\_\_\_\_\_\) - Option B: - The critical values are \(\pm \_\_\_\_\_\_\_\_\) **Identify the rejection region(s):** Choose the correct answer below. - Option A: - Fail to reject \(H_0\). - Option B: - Fail to reject \(H_a\). - Option C: - Fail to reject \(H_1\).
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