A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test thıs claim. During your test you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 50.7 milligrams. Assume the population is normally distributed an the population standard deviation is 7.9 milligrams. At a = 0.03, can you reject the company's claim? Complete parts (a) through (e). ..... A. The critical values are + 2.17 O B. The critical value is Identify the rejection region(s). Choose the correct answer below. O A. O B. Q Fail to reject Ho Fail to reject Ho. Fail to reject Ho- Reject Ho. Reject Hg- Reject Ho Reject Ho. (c) Find the standardized test statistic. (Round to two decimal places as needed.)
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 50 milligrams. You want to test thıs claim. During your test you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 50.7 milligrams. Assume the population is normally distributed an the population standard deviation is 7.9 milligrams. At a = 0.03, can you reject the company's claim? Complete parts (a) through (e). ..... A. The critical values are + 2.17 O B. The critical value is Identify the rejection region(s). Choose the correct answer below. O A. O B. Q Fail to reject Ho Fail to reject Ho. Fail to reject Ho- Reject Ho. Reject Hg- Reject Ho Reject Ho. (c) Find the standardized test statistic. (Round to two decimal places as needed.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![### Hypothesis Testing: Cola Caffeine Content
A company claims that the average caffeine content of a 12-ounce bottle of cola is 50 milligrams. To verify this claim, a test is conducted with a random sample of thirty 12-ounce cola bottles, which shows an average caffeine content of 50.7 milligrams. Assuming a normally distributed population with a standard deviation of 7.9 milligrams, we need to determine whether this sample provides sufficient evidence to reject the company’s claim at a significance level (\(\alpha\)) of 0.03.
#### Problem Breakdown:
1. **Critical Values:**
- The critical values are \(\pm 2.17\).
2. **Rejection Regions:**
- **Figure Descriptions:**
- **Diagram A:** Displays a normal distribution curve with labeled regions showing where the null hypothesis (\(H_0\)) is rejected. The rejection region is on the left side of the curve.
- **Diagram B:** Similar distribution, but the rejection region is on the right side.
- **Diagram C:** Displays two-tailed rejection regions on both sides of the curve, indicating areas where \(H_0\) is rejected.
- **Correct Answer:** Diagram C is marked as correct, indicating a two-tailed test with rejection regions on both ends.
3. **Standardized Test Statistic:**
- To be calculated: \( z = \) [box for input] (rounded to two decimal places as needed).
Use this information to determine if the sample mean significantly differs from the claimed mean of 50 milligrams. The critical values indicate the thresholds for rejection in a two-tailed test. Calculate the \(z\)-score to see where it falls relative to these critical values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7226e99-cda6-474c-a507-35a166b04cf3%2F5d99e9e6-b8c8-4678-82c8-08ac431658f0%2Fa3nj6i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Cola Caffeine Content
A company claims that the average caffeine content of a 12-ounce bottle of cola is 50 milligrams. To verify this claim, a test is conducted with a random sample of thirty 12-ounce cola bottles, which shows an average caffeine content of 50.7 milligrams. Assuming a normally distributed population with a standard deviation of 7.9 milligrams, we need to determine whether this sample provides sufficient evidence to reject the company’s claim at a significance level (\(\alpha\)) of 0.03.
#### Problem Breakdown:
1. **Critical Values:**
- The critical values are \(\pm 2.17\).
2. **Rejection Regions:**
- **Figure Descriptions:**
- **Diagram A:** Displays a normal distribution curve with labeled regions showing where the null hypothesis (\(H_0\)) is rejected. The rejection region is on the left side of the curve.
- **Diagram B:** Similar distribution, but the rejection region is on the right side.
- **Diagram C:** Displays two-tailed rejection regions on both sides of the curve, indicating areas where \(H_0\) is rejected.
- **Correct Answer:** Diagram C is marked as correct, indicating a two-tailed test with rejection regions on both ends.
3. **Standardized Test Statistic:**
- To be calculated: \( z = \) [box for input] (rounded to two decimal places as needed).
Use this information to determine if the sample mean significantly differs from the claimed mean of 50 milligrams. The critical values indicate the thresholds for rejection in a two-tailed test. Calculate the \(z\)-score to see where it falls relative to these critical values.
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