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 ? = 64 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. H0: ? ≠ 64; H1: ? = 64H0: ? = 64; H1: ? ≠ 64 H0: ? = 64; H1: ? > 64H0: ? < 64; H1: ? = 64H0: ? = 64; H1: ? < 64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution and ? is known.The Student's t, since we assume that x has a normal distribution and ? is known. The standard normal, since we assume that x has a normal distribution and ? is unknown.The Student's t, since we assume that x has a normal distribution and ? is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 ? = 64 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.

H₀: ? ≠ 64; H₁: ? = 64H₀: ? = 64; H₁: ? ≠ 64 H₀: ? = 64; H₁: ? > 64H₀: ? < 64; H₁: ? = 64H₀: ? = 64; H₁: ? < 64

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution and ? is known.The Student's t, since we assume that x has a normal distribution and ? is known. The standard normal, since we assume that x has a normal distribution and ? is unknown.The Student's t, since we assume that x has a normal distribution and ? is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250 0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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