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A study examined the fat content (in grams) for samples of beef and meat hot dogs. The resulting 98% confidence interval for HMeat - HBeef is (1.8,4.8). Complete parts a) through c) below. a) The endpoints of this confidence interval are positive numbers. What does that indicate? O A. The type of hot dog with a higher mean fat content cannot be determined. O B. The mean fat content is probably higher for meat hot dogs. OC. The mean fat contents for each type of hot dog varies greatly from the other. O D. The mean fat content is probably higher for beef hot dogs. b) What does the fact that the confidence interval does not contain 0 indicate? O A. There is no difference between the two samples. O B. The difference in the two sample means is insignificant. OC. Both samples have a lot of variation. O D. The difference in the two sample means is significant. c) If we use this confidence interval to test the hypothesis that uMeat - HReef = 0, what's the corresponding alpha level?

A study examined the fat content (in grams) for samples of beef and meat hot dogs. The resulting 98% confidence interval for HMeat - HBeef is (1.8,4.8). Complete parts a) through c) below. a) The endpoints of this confidence interval are positive numbers. What does that indicate? O A. The type of hot dog with a higher mean fat content cannot be determined. O B. The mean fat content is probably higher for meat hot dogs. OC. The mean fat contents for each type of hot dog varies greatly from the other. O D. The mean fat content is probably higher for beef hot dogs. b) What does the fact that the confidence interval does not contain 0 indicate? O A. There is no difference between the two samples. O B. The difference in the two sample means is insignificant. OC. Both samples have a lot of variation. O D. The difference in the two sample means is significant. c) If we use this confidence interval to test the hypothesis that uMeat - HReef = 0, what's the corresponding alpha level?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**A Study on Fat Content in Hot Dogs: Confidence Interval Insights** A study examined the fat content (in grams) for samples of beef and meat hot dogs. The resulting 98% confidence interval for the difference in mean fat content, \(\mu_{Meat} - \mu_{Beef}\), is (1.8, 4.8). Below, we explore what this confidence interval implies: ### a) Interpretation of Positive Endpoints The endpoints of this confidence interval, both positive numbers, indicate: - **A.** The type of hot dog with a higher mean fat content cannot be determined. - **B.** The mean fat content is probably higher for meat hot dogs. - **C.** The mean fat contents for each type of hot dog varies greatly from the other. - **D.** The mean fat content is probably higher for beef hot dogs. **Correct Answer: B.** The mean fat content is probably higher for meat hot dogs. This is because the entire interval is above zero, suggesting that meat hot dogs have a higher mean fat content than beef hot dogs. ### b) Implications of Confidence Interval Not Containing 0 What does the fact that the confidence interval does not contain 0 indicate? - **A.** There is no difference between the two samples. - **B.** The difference in the two sample means is insignificant. - **C.** Both samples have a lot of variation. - **D.** The difference in the two sample means is significant. **Correct Answer: D.** The difference in the two sample means is significant, as the interval does not include zero. ### c) Determining the Alpha Level If this confidence interval is used to test the hypothesis that \(\mu_{Meat} - \mu_{Beef} = 0\), what is the corresponding alpha level? Since this is a 98% confidence interval, the alpha level, which represents the probability of rejecting a true null hypothesis, is: \[ \alpha = 100\% - 98\% = 2\%. \] Therefore, the corresponding alpha level is 2%. This study guide provides interpretation and understanding of confidence intervals in the context of comparing two sample means, a fundamental concept in inferential statistics.
Transcribed Image Text:**A Study on Fat Content in Hot Dogs: Confidence Interval Insights** A study examined the fat content (in grams) for samples of beef and meat hot dogs. The resulting 98% confidence interval for the difference in mean fat content, \(\mu_{Meat} - \mu_{Beef}\), is (1.8, 4.8). Below, we explore what this confidence interval implies: ### a) Interpretation of Positive Endpoints The endpoints of this confidence interval, both positive numbers, indicate: - **A.** The type of hot dog with a higher mean fat content cannot be determined. - **B.** The mean fat content is probably higher for meat hot dogs. - **C.** The mean fat contents for each type of hot dog varies greatly from the other. - **D.** The mean fat content is probably higher for beef hot dogs. **Correct Answer: B.** The mean fat content is probably higher for meat hot dogs. This is because the entire interval is above zero, suggesting that meat hot dogs have a higher mean fat content than beef hot dogs. ### b) Implications of Confidence Interval Not Containing 0 What does the fact that the confidence interval does not contain 0 indicate? - **A.** There is no difference between the two samples. - **B.** The difference in the two sample means is insignificant. - **C.** Both samples have a lot of variation. - **D.** The difference in the two sample means is significant. **Correct Answer: D.** The difference in the two sample means is significant, as the interval does not include zero. ### c) Determining the Alpha Level If this confidence interval is used to test the hypothesis that \(\mu_{Meat} - \mu_{Beef} = 0\), what is the corresponding alpha level? Since this is a 98% confidence interval, the alpha level, which represents the probability of rejecting a true null hypothesis, is: \[ \alpha = 100\% - 98\% = 2\%. \] Therefore, the corresponding alpha level is 2%. This study guide provides interpretation and understanding of confidence intervals in the context of comparing two sample means, a fundamental concept in inferential statistics.
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