(a) To remedy this issue, Congress has passed a law that the salinity of the Colorado river as it passes into Mexico cannot be above 145 ppm on average. Perform a hypothesis test with a confidence level of 95% to test the claim and provide the p-value. (b) If the actual water salinity is µa = 152 ppm and the σ = 2.1ppm what’s the probability of committing a type II error, β. (c) If the actual population mean µa = 152 ppm σ = 2.1ppm, what’s the sample size needed for β = 0.1?
Throughout the 20th century, a huge amount of water has been diverted from the Colorado river in the US for irrigation purposes, leaving the remaining river much higher in salinity. This water has often
been saline enough that it is useless to Mexico for irrigation purposes. 49 water samples are collected
| salinityppm | |
| 1 | 148.51 |
| 2 | 144.91 |
| 3 | 144.96 |
| 4 | 148.55 |
| 5 | 145.8 |
| 6 | 143.84 |
| 7 | 146.78 |
| 8 | 146.11 |
| 9 | 146.41 |
| 10 | 147.21 |
| 11 | 145.62 |
| 12 | 147.75 |
| 13 | 145.94 |
| 14 | 147.1 |
| 15 | 148.7 |
| 16 | 147.31 |
| 17 | 145.72 |
| 18 | 148.81 |
| 19 | 148.49 |
| 20 | 147.55 |
| 21 | 146.9 |
| 22 | 145.08 |
| 23 | 149.26 |
| 24 | 145.14 |
| 25 | 150.99 |
| 26 | 149.62 |
| 27 | 145.91 |
| 28 | 144.24 |
| 29 | 144.91 |
| 30 | 146.94 |
| 31 | 145.88 |
| 32 | 145.67 |
| 33 | 144.4 |
| 34 | 146.31 |
| 35 | 144.75 |
| 36 | 142.9 |
| 37 | 145.6 |
| 38 | 148.33 |
| 39 | 145.19 |
| 40 | 147.68 |
| 41 | 143 |
| 42 | 146.28 |
| 43 | 147.49 |
| 44 | 147.03 |
| 45 | 146.62 |
| 46 | 145.05 |
| 47 | 144.62 |
| 48 | 144.25 |
| 49 | 146.65 |
(a) To remedy this issue, Congress has passed a law that the salinity of the Colorado river as it passes into Mexico cannot be above 145 ppm on average. Perform a hypothesis test with a confidence level of 95% to test the claim and provide the p-value.
(b) If the actual water salinity is µa = 152 ppm and the σ = 2.1ppm what’s the probability of committing a type II error, β.
(c) If the actual population mean µa = 152 ppm σ = 2.1ppm, what’s the sample size needed for β = 0.1?
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