Question

A quality characteristic of interest for a​ tea-bag-filling process is the weight of the tea in the individual bags. The label weight on the package indicates that the mean amount is 5.465.46 grams of tea in a bag. Problems arise if the bags are underfilled or if the mean amount of tea in a bag exceeds the label weight. The accompanying data are the​ weights, in​ grams, of a sample of 5050 tea bags produced in one hour by a single machine. Complete parts​ (a) through​ (c) below.

Tea Bags weight data

5.13
5.17
5.21
5.22
5.22
5.26
5.27
5.28
5.28
5.28
5.32
5.32
5.32
5.34
5.35
5.34
5.34
5.33
5.38
5.37
5.37
5.38
5.41
5.40
5.38
5.41
5.43
5.44
5.43
5.44
5.44
5.43
5.44
5.43
5.43
5.44
5.46
5.44
5.45
5.48
5.46
5.48
5.50
5.50
5.53
5.51
5.54
5.57
5.55
5.65

(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 5.465.46

​grams?

The company IS OR IS NOT meeting the requirement set forth on the label that the mean amount of tea in a bag is 5.465.46 ​grams since 5.465.46 IS OR IS NOT

contained within the interval.

(c) Do you think the assumption needed to construct the confidence interval estimate in​ (a) is​ valid?

The assumption needed to construct the confidence interval estimate in​ (a) is that at least five tea bags are below the target OR the sample standard deviation is equal to the population standard deviation OR the weights are normally distributed OR the weights are uniformly distributed. This assumption CAN OR CANNOT be considered​ valid, based on the boxplot and normal probability plot OR information provided in the problem statement.​

Answer 1

(c)

The assumption needed to construct the confidence interval estimate in​ the weights are normally distributed.

This assumption CAN be considered​ valid, based on the boxplot and normal probability plot.