8.2 In Class

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Hennepin Technical College *

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2010

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Civil Engineering

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Oct 30, 2023

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Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of 𝜇 = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water crops. This well is tested on a regular basis for arsenic. A random sample of 37 tests gave a sample mean of 7.2 ppb arsenic, with ? = 1.9 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb. Use a level of significance of 1%. 𝜶 = ?. ?? 𝑯 𝑶 : 𝝁 = ?. ? 𝑯 ? : 𝝁 < ?. ? 𝒅. 𝒇. = ?? 𝒕 = ?. ? − ?. ? ?. ? √?? = −?. ???? P-value method: (Row 35, 2.56 falls in between 2.438 and 2.724, follow those up to one-tail row) 0.005 < 𝑝 − ?𝑎𝑙?𝑒 < 0.010 𝑝 − ?𝑎𝑙?𝑒 𝑖𝑛?𝑒??𝑎𝑙 ≤ 𝛼 Or Critical Value method: (One tail, 0.01, down to row 35) Critical Value = −2.438 Test statistic is in the Rejection Region (it is farther away from zero than the critical value is) Reject 𝐇 𝐎 At the 1% significance level, the sample data indicates that the mean level of arsenic in the well is less than 8 ppb.
Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung a professor of civil engineering at the University of British Columbia. Slab avalanches studied in Canada have an average thickness of 𝜇 = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of 16 avalanches in the spring gave a mean of 61.8 cm with ? = 10.6 cm. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in Canada. 𝜶 = ?. ?? 𝑯 𝑶 : 𝝁 = ?? 𝑯 ? : 𝝁 ≠ ?? 𝒅. 𝒇. = ?? 𝒕 = ??. ? − ?? ??. ? √?? = −?. ???? P-value method: (Row 15, 1.9623 falls in between 1.753 and 2.131, follow those up to two tail row) 0.05 < 𝑝 − ?𝑎𝑙?𝑒 < 0.10 𝑝 − ?𝑎𝑙?𝑒 𝑖𝑛?𝑒??𝑎𝑙 > 𝛼 Or Critical Value method: (Two tail, 0.01, down to row 15) Critical Value = ±2.947 Test statistic is not in the Rejection Region (it is closer to zero than the critical value is) Fail to Reject 𝑯 𝑶 At the 1% significance level, there is insufficient data to say that the mean slab thickness in the Vail Region is different from that in Canada.
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