Question

g Refer to the Environmental Geology (Vol.58, 2009) simulation study of how far a block from a collapsing rockwall will bounce down a soil solpe. Rebound lengths (in meters) were estimated for 13 rock bounces. The data are presented below. Consider a test of hypothesis for the variation in rebound lengths for the theoretical population of rock bounces form the collapsing rockwall. In particular, a geologist wants to determine if the variance differs from 10 m 2. 10.94 13.71 11.38 7.26 17.83 11.92 11.87 5.44 13.35 4.90 5.85 5.10 6.77 a. Specify the null and alternative hypotheses. Be sure to define the parameter used in your hypotheses. b. Compute the value of the test statistic. c. Determine the rejection region for the test using alpha

Answer 1

H0 : σ² = 10

H1 : σ² ≠ 10

X² = 20.124

Pvalue = 0.064776

there is significant evidence to conclude that the rebound lengtb of rockfall down a slope is not 10m²

Explanation:

Given the data:

10.94 13.71 11.38 7.26 17.83 11.92 11.87 5.44 13.35 4.90 5.85 5.10 6.77

Using a calculator ;

The sample variance, s² = 16.77

α = 0.10

The null and alternative hypothesis :

H0 : σ² = 10

H1 : σ² ≠ 10

The test statistic :

X² = [(n - 1)*s² ÷ σ²]

s² = 16.77

n = sample size = 13 ; s²

X² = [(13 -1)*16.77 ÷ 10

X² = (12 * 16.77) / 10

X² = 201.24 / 10

X² = 20.124

The Pvalue using a Pvalue calculator ; degree of freedom (df) = 13 - 1 = 12

Pvalue = 0.064776

Pvalue < α ; Hence we reject the null

Hence, there is significant evidence to conclude that the rebound lengtb of rockfall down a slope is not 10m²