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雷达卡
8.65
A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount is 5.5 grams of tea in a bag. If the bags are under filled, two problems arise. First, customers may not be able to brew the tea to be as strong as they wish. Second, the company may be in violation of the truth-in-labeling laws. On the other hand, if the mean amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory,
differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 170 bags per minute). The following data (stored in Teabags ) are the weights, in grams, of a sample of 50 tea bags produced in one hour by a single machine:
茶叶填充过程中的一项质量指标是茶叶袋中的茶叶分量。茶叶包装袋上的说明显示，平均每包茶叶的质量为 5.5 克。一方面如果茶叶袋中茶叶的分量不足，就会产生两个问题。首先，消费者不能冲泡出足够浓的茶水。第二，公司违反真实标签法。然而另一方面，如果袋中茶叶平均分量过多，那么公司就是在免费送茶叶。但是由于工厂中温度、湿度波动，茶叶密度，以及机器填充操作 (每分钟大约填充 170包)的误差影响，不太可能实现每包茶叶分量都正好。以下 (存储在文件 Teabags 中)提供了从某台机器 1小时内填充的茶叶袋中随机选择50包组成的样本数据 (克)。
5.65 | 5.44 | 5.42 | 5.40 | 5.53 | 5.34 | 5.54 | 5.45 | 5.52 | 5.41 |
5.57 | 5.40 | 5.53 | 5.54 | 5.55 | 5.62 | 5.56 | 5.46 | 5.44 | 5.51 |
5.47 | 5.40 | 5.47 | 5.61 | 5.53 | 5.32 | 5.67 | 5.29 | 5.49 | 5.55 |
5.77 | 5.57 | 5.42 | 5.58 | 5.58 | 5.50 | 5.32 | 5.50 | 5.53 | 5.58 |
5.61 | 5.45 | 5.44 | 5.25 | 5.56 | 5.63 | 5.50 | 5.57 | 5.67 | 5.36 |
a. Construct a 99% confidence interval estimate for the population mean weight of the tea bags.
b. Is the company meeting the requirement set forth on the label that the mean amount of tea in a bag is 5.5 grams?
c. Do you think the assumption needed to construct the confidence interval estimate in (a) is valid?
a.构建茶叶袋总体的平均重量的 99%的置信区间。
b.公司是否符合包装袋上平均 5.5 克的承诺?
c.为建立 (a) 中置信区间的相关假设是否合理?
clear all
set more off
cap log use
/*导入数据*/
import excel "D:\ \Teabags.xlsx", sheet("Sheet1") firstrow clear
/*对数据进行描述*/
describe
summarize
/*已知均值和标准差，求99%置信区间*/
ci means
ttest Teabags=5.5014, level(99)
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