A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 9.5, 9.7, 9.6, and 9.8 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. Answer parts a and b below. a. Choose the correct interpretation of the confidence interval below and, if necessary, fill in the answer boxes to complete your choice. O A. We are 95% confident that the sample mean is between B. There is a 95% chance that all intervals will be between and and C. We are 95% confident the population mean is between and D. The requirements for constructing a confidence interval are not satisfied.
A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 9.5, 9.7, 9.6, and 9.8 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. Answer parts a and b below. a. Choose the correct interpretation of the confidence interval below and, if necessary, fill in the answer boxes to complete your choice. O A. We are 95% confident that the sample mean is between B. There is a 95% chance that all intervals will be between and and C. We are 95% confident the population mean is between and D. The requirements for constructing a confidence interval are not satisfied.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Educational Content: Confidence Intervals and Hypothesis Testing**
In this exercise, a statistics instructor examined four bags of oranges, each labeled as weighing 10 pounds. However, the actual weights of the bags were 9.5, 9.7, 9.6, and 9.8 pounds. Assuming a normal distribution of weights, the task is to determine a 95% confidence interval for the mean weight of all bags of oranges using technology for calculations. Below are the steps and questions to consider.
### Part a: Confidence Interval Interpretation
**Question:** Choose the correct interpretation of the confidence interval below and, if necessary, fill in the blanks.
- **A.** We are 95% confident that the sample mean is between [ ] and [ ].
- **B.** There is a 95% chance that all intervals will be between [ ] and [ ].
- **C.** We are 95% confident the population mean is between [ ] and [ ].
- **D.** The requirements for constructing a confidence interval are not satisfied.
(*Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.*)
### Part b: Hypothesis Testing
**Question:** Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer.
- **A.** No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the interval.
- **B.** Yes, it does capture 10. Reject the claim of 10 pounds because 10 is in the interval.
- **C.** Yes, it does capture 10. Do not reject the claim of 10 pounds because 10 is in the interval.
- **D.** No, it does not capture 10. Do not reject the claim of 10 pounds because 10 is not in the interval.
**Explanation:**
- **Confidence Interval Interpretation:** A confidence interval provides a range within which we can be certain the population parameter lies. In this case, option C is aligned with the correct interpretation, focusing on the population mean.
- **Hypothesis Testing:** The hypothesis test determines if there is enough evidence to support or reject a given claim. If the interval does not include 10 pounds, we may reject the null hypothesis. If it includes 10, we fail to reject it.
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Transcribed Image Text:**Educational Content: Confidence Intervals and Hypothesis Testing**
In this exercise, a statistics instructor examined four bags of oranges, each labeled as weighing 10 pounds. However, the actual weights of the bags were 9.5, 9.7, 9.6, and 9.8 pounds. Assuming a normal distribution of weights, the task is to determine a 95% confidence interval for the mean weight of all bags of oranges using technology for calculations. Below are the steps and questions to consider.
### Part a: Confidence Interval Interpretation
**Question:** Choose the correct interpretation of the confidence interval below and, if necessary, fill in the blanks.
- **A.** We are 95% confident that the sample mean is between [ ] and [ ].
- **B.** There is a 95% chance that all intervals will be between [ ] and [ ].
- **C.** We are 95% confident the population mean is between [ ] and [ ].
- **D.** The requirements for constructing a confidence interval are not satisfied.
(*Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.*)
### Part b: Hypothesis Testing
**Question:** Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer.
- **A.** No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the interval.
- **B.** Yes, it does capture 10. Reject the claim of 10 pounds because 10 is in the interval.
- **C.** Yes, it does capture 10. Do not reject the claim of 10 pounds because 10 is in the interval.
- **D.** No, it does not capture 10. Do not reject the claim of 10 pounds because 10 is not in the interval.
**Explanation:**
- **Confidence Interval Interpretation:** A confidence interval provides a range within which we can be certain the population parameter lies. In this case, option C is aligned with the correct interpretation, focusing on the population mean.
- **Hypothesis Testing:** The hypothesis test determines if there is enough evidence to support or reject a given claim. If the interval does not include 10 pounds, we may reject the null hypothesis. If it includes 10, we fail to reject it.
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