Question 10
“Aqua Aqua (AA)” is a manufacturer of water purifiers. AA wants to understand the life of its RO filters. The life of a filter is measured in terms of “Litres of Water Purified (LWP)” before a warning light is raised for maintenance. A sample of 20 water purifiers were tested and the time (LWP) after which the warning light is raised for maintenance of the RO Filter was noted (data provided in Table-2). With this data, AA wants to understand the possible distribution for the life of the RO filter. To this end, it is proposed to bin the data in 4 groups “Low Life (LWP <=25)”, “Medium Life (25<LWP<=40)”, “High Life (40<LWP<=80)”, “Excellent Life (LWP>80)”.
The following Ф values are given to you, where Ф(z) indicates the area under the curve (between “0” to “LWP”) for a normal distribution with a mean of 60 and standard deviation of 24. Ф(-1.45) = 0.07; Ф(-0.83) = 0.20; Ф(+0.83) = 0.79; Ф(+1.45) = 0.93
| Sample-ID | RO Filter Life (in LWP) | Sample-ID | RO Filter Life (in LWP) |
|---|---|---|---|
| S-1 | 73 | S-11 | 70 |
| S-2 | 49 | S-12 | 47 |
| S-3 | 12 | S-13 | 78 |
| S-4 | 72 | S-14 | 15 |
| S-5 | 97 | S-15 | 54 |
| S-6 | 95 | S-16 | 61 |
| S-7 | 79 | S-17 | 91 |
| S-8 | 42 | S-18 | 61 |
| S-9 | 70 | S-19 | 26 |
| S-10 | 53 | S-20 | 64 |
Table-2
Given this information, answer the subquestions
Assume that a common value of 8.79 is identified for the tabulated test statistic (for both uniform and normal distribution tests), then (choose all that is applicable)
REJECT the null hypothesis and conclude that the life of the RO filter is not UNIFORMLY distributed
At the specified significance level, REJECT the null hypothesis and conclude that the life of the RO filter is not UNIFORMLY distributed
REJECT the null hypothesis and conclude that the life of the RO filter is not NORMALY distributed
At the specified significance level, REJECT the null hypothesis and conclude that the life of the RO filter is not NORMALY distributed
DO NOT REJECT the null hypothesis and conclude that the life of the RO filter is UNIFORMLY distributed
At the specified significance level, DO NOT REJECT the null hypothesis and conclude that the life of the RO filter is UNIFORMLY distributed
DO NOT REJECT the null hypothesis and conclude that the life of the RO filter is NORMALY distributed
At the specified significance level, DO NOT REJECT the null hypothesis and conclude that the life of the RO filter is NORMALLY distributed