Hi, I would appreciate if you could help me with the following question please. ### Confidence Interval for the Average Weight of PomelosThe weight of a pomelo is normally distributed. A consumer is interested in the average weight of pomelos. In a random sample of twelve pomelos, the average weight is determined to be 1301 g with a standard deviation of 168 g. Based on this data, construct a 99% confidence interval for the population mean weight.Which of the following intervals is the correct 99% confidence interval for the population mean weight of pomelos?a. (1257.5160, 1344.4840) b. (1150.3670, 1451.6330) c. (1152.8404, 1449.1596) d. (1176.0706, 1425.9294)---#### Solution Approach:To calculate the 99% confidence interval for the mean, we can use the formula for the confidence interval for the mean when the population standard deviation is unknown:\[ \bar{x} \pm t \times \left( \frac{s}{\sqrt{n}} \right) \]Where:- $ \bar{x} $ is the sample mean (1301 g)- $ t $ is the t-value from the t-distribution table corresponding to 99% confidence level and degrees of freedom $ df = n - 1 $ (in this case, $ df = 12 - 1 = 11 $)- $ s $ is the sample standard deviation (168 g)- $ n $ is the sample size (12)By comparing the calculated interval to the answer choices, you can determine the correct confidence interval for the population mean weight of pomelos.

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The weight of a pomelo is normally distributed. A consumer is interested in the average weight of pomelos. In a random sample of twelve pomelos, the average weight is determined to be 1301 g with a standard deviation of 168 g. Construct a 99% confidence interval for the population mean weight. O a. (1257.5160, 1344.4840) O b. (1150.3670, 1451.6330) c. (1152.8404, 1449.1596) o d. (1176.0706, 1425.9294)

The weight of a pomelo is normally distributed. A consumer is interested in the average weight of pomelos. In a random sample of twelve pomelos, the average weight is determined to be 1301 g with a standard deviation of 168 g. Construct a 99% confidence interval for the population mean weight. O a. (1257.5160, 1344.4840) O b. (1150.3670, 1451.6330) c. (1152.8404, 1449.1596) o d. (1176.0706, 1425.9294)

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Concept explainers

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Hi, I would appreciate if you could help me with the following question please.

### Confidence Interval for the Average Weight of Pomelos

The weight of a pomelo is normally distributed. A consumer is interested in the average weight of pomelos. In a random sample of twelve pomelos, the average weight is determined to be 1301 g with a standard deviation of 168 g. Based on this data, construct a 99% confidence interval for the population mean weight.

Which of the following intervals is the correct 99% confidence interval for the population mean weight of pomelos?

a. (1257.5160, 1344.4840)
b. (1150.3670, 1451.6330)
c. (1152.8404, 1449.1596)
d. (1176.0706, 1425.9294)

---

#### Solution Approach:

To calculate the 99% confidence interval for the mean, we can use the formula for the confidence interval for the mean when the population standard deviation is unknown:

\[ \bar{x} \pm t \times \left( \frac{s}{\sqrt{n}} \right) \]

Where:
- $ \bar{x} $ is the sample mean (1301 g)
- $ t $ is the t-value from the t-distribution table corresponding to 99% confidence level and degrees of freedom $ df = n - 1 $ (in this case, $ df = 12 - 1 = 11 $)
- $ s $ is the sample standard deviation (168 g)
- $ n $ is the sample size (12)

By comparing the calculated interval to the answer choices, you can determine the correct confidence interval for the population mean weight of pomelos.

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