Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called th slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of µ = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm). 59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x3= cm S= cm (ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada. (a) What is the level of significance? State the null and alternate hypotheses. Ο H: μ-67; H1f μ <67| Ο H μ- 67; H1: μ - 67 Ο H μ=67; Hi: μ >67 Ο H: μ < 67; Hi: μ -67 Ο H: μ 67; Η: μ = 67 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is known. O The standard normal, since we assume that x has a normal distribution and o is unknown. O The Student's t, since we assume that x has a normal distribution and o is known. O The Student's t, since we assume that x has a normal distribution and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called th slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Suppose slab avalanches studied in a region of Canada had an average thickness of µ = 67 cm. The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm). 59 51 76 38 65 54 49 62 68 55 64 67 63 74 65 79 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x3= cm S= cm (ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in the region of Canada. (a) What is the level of significance? State the null and alternate hypotheses. Ο H: μ-67; H1f μ <67| Ο H μ- 67; H1: μ - 67 Ο H μ=67; Hi: μ >67 Ο H: μ < 67; Hi: μ -67 Ο H: μ 67; Η: μ = 67 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is known. O The standard normal, since we assume that x has a normal distribution and o is unknown. O The Student's t, since we assume that x has a normal distribution and o is known. O The Student's t, since we assume that x has a normal distribution and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. O P-value > 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Transcribed Image Text: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.
Suppose slab avalanches studied in a region of Canada had an average thickness of u = 67 cm. The ski patrol at Vail, Colorado, is studying
slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm).
59 51 76 38 65 54 49 62
68 55 64 67 63
74 65 79
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
X=
cm
S=
cm
(ii) Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab
thickness in the Vail region is different from that in the region of Canada.
(a) What is the level of significance?
State the null and alternate hypotheses.
Ο Hρ: μ= 67; H μ < 67
Ο Hρ: μ= 67; H μ.67
Ο Hρ: μ= 67; H: μ > 67
Ο H: μ < 67; H1: μ - 67
Ο H: μ 67; Η: μ= 67
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since we assume that x has a normal distribution and o is known.
The standard normal, since we assume that x has a normal distribution and o is unknown.
O The Student's t, since we assume that x has a normal distribution and o is known.
O The Student's t, since we assume that x has a normal distribution and o is unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate the P-value.
O P-value > 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
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