Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately ?2 = 136.2. Suppose that for the past 8 years, the variance has been s2 = 110.6. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. (a) What is the level of significance? State the null and alternate hypotheses. H0: ?2 = 136.2; H1: ?2 < 136.2H0: ?2 < 136.2; H1: ?2 = 136.2 H0: ?2 = 136.2; H1: ?2 > 136.2H0: ?2 = 136.2; H1: ?2 ≠ 136.2 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a normal population distribution.We assume a exponential population distribution. We assume a binomial population distribution.We assume a uniform population distribution. (c) Find or estimate the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that the variance for number of mountain climber deaths is less than 136.2At the 1% level of significance, there is sufficient evidence to conclude that the variance for number of mountain climber deaths is less than 136.2

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Description: Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately ?2 = 136.2. Suppose that for the past 8 years, the variance has been s2 = 110.6. Use a 1% level of significance to test the claim that the

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately ?² = 136.2. Suppose that for the past 8 years, the variance has been s² = 110.6. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?² = 136.2; H₁: ?² < 136.2H₀: ?² < 136.2; H₁: ?² = 136.2 H₀: ?² = 136.2; H₁: ?² > 136.2H₀: ?² = 136.2; H₁: ?² ≠ 136.2

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

What assumptions are you making about the original distribution?

We assume a normal population distribution.We assume a exponential population distribution. We assume a binomial population distribution.We assume a uniform population distribution.

P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to conclude that the variance for number of mountain climber deaths is less than 136.2At the 1% level of significance, there is sufficient evidence to conclude that the variance for number of mountain climber deaths is less than 136.2

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