High School

1. A local butcher has been investigating the difference in the weights of lambs in his shop both before and after preparation. The market states a lamb should weigh an average of 135 pounds (lb), but he believes the processing of the meat is causing a loss of more than 5 pounds (lb) of meat. He has collected the following data on 12 different lambs he has processed over the last month:

- **Lamb #1**
- Pre-processed weight: 125 lb
- Post-processed weight: 120 lb

- **Lamb #2**
- Pre-processed weight: 138 lb
- Post-processed weight: 130 lb

- **Lamb #3**
- Pre-processed weight: 147 lb
- Post-processed weight: 138 lb

- **Lamb #4**
- Pre-processed weight: 156 lb
- Post-processed weight: 154 lb

- **Lamb #5**
- Pre-processed weight: 125 lb
- Post-processed weight: 121 lb

- **Lamb #6**
- Pre-processed weight: 120 lb
- Post-processed weight: 112 lb

- **Lamb #7**
- Pre-processed weight: 134 lb
- Post-processed weight: 125 lb

- **Lamb #8**
- Pre-processed weight: 152 lb
- Post-processed weight: 144 lb

- **Lamb #9**
- Pre-processed weight: 145 lb
- Post-processed weight: 141 lb

- **Lamb #10**
- Pre-processed weight: 141 lb
- Post-processed weight: 133 lb

- **Lamb #11**
- Pre-processed weight: 119 lb
- Post-processed weight: 110 lb

- **Lamb #12**
- Pre-processed weight: 133 lb
- Post-processed weight: 122 lb

(a) Are these data sets independent? Explain.

(b) Perform the butcher's test at a 95% confidence level. Up to what value could we reject the null hypothesis?

Answer :

The data sets are independent as the pre-processing and post-processing weights are not influenced by each other. We can perform a paired t-test with a significance level of 0.05 to see if the weight loss is significant. The actual value up to which we could reject the null hypothesis would depend on the results of the t-test.

(a) The data sets are independent as the pre-processing weight and the post-processing weight of the lamb are not influenced by each other. The weight after processing does not depend upon the pre-processing weight but rather on the amount of fats and other non-meat parts that are removed during processing.

(b) For the butcher's test, we should perform a paired t-test considering the significance level of 0.05 (since the confidence level is 95%). A paired t-test compares the means of the two related groups (in this case pre-processed and post-processed weight).

We can reject the null hypothesis if the p-value is less than the significance level (0.05). Calculation of this requires statistical software or manual calculation incorporating the pre-processing and post-processing weights.

Learn more about the topic of Paired t-Test here:

https://brainly.com/question/31829815

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