Oasis Inc. which produces water wants to analyze the mineralcontents (gm) in the bottle of 1 liter water they produce.Especially, they are interested in identifying the magnesiumcontents, which is one of the most important minerals in the water.The quality control engineer at their production unit randomlyselected 7 bottles and then measured the mineral contents in thesamples. The results obtained from the samples are as shown in thetable below:
Sample#
Magnesium weight (gm)
1
11.3 + ……..=…….
2
12.2
3
11.7+……..= ……..
4
12.9
5
12.5+…….=……….
6
11.7
7
12.6
To obtain the weight for sample 1, sample 3 and sample 5 inthe table, follow the instruction below:
If the fourth number of your student ID is in between:
- (0 & 3), then add 0.2 to the weight as shown in thetable for samples 1, 3 and 5.
- (4 & 6), then add 0.6 to the weight as shown in thetable for samples 1, 3 and 5.
- (7 & 9), then add 0.9 to the weight as shown in thetable for samples 1, 3 and 5.
Fourth number is 5
For example, if student ID: 116523, then add 0.6 in the givendata for samples 1, 3 and 5:
- Sample 1=11.3+0.6 =11.9
- Sample 3 = 11.7 +0.6 = 12.3
- Sample 5 = 12.5+0.6 = 13.1
a. Assuming that the population standard deviation is similarto the standard deviation obtained from the above samples, identifythe bounds at ….. % confidence interval (CI)?
(4.0)
Note: If the last number of your student ID is inbetween:
- (0 & 2), then put CI as 92%
- (3 & 5), then put CI as 94%
- (6 & 7), then put CI as 96%
- (8 & 9), then put CI as 98%
Last number is 3
For example, if student ID: 116523, then CI = 94%.
b. If only one sided confidence bound is desired by thecompany at the lower tail, then what will be the lower bound forthe date at the CI similar to (a). Discuss the difference in thelower bound as compared to (a) and give reason for the differenceusing simple figure(s).
(3.0)
c. If the company wants to have an error of less than 0.20 inestimating the magnesium content, then what sample size should thecompany use in part (b) for the analysis? (2.0)
ID=114985
