Question

Let x represent the number of mountain climbers killed each year. The long- term

variance of x is approximately σ2 =136.2. Suppose that for the past 8 years, the variance

has been s = 115.1. 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.

Answer 1

Null hypothesis $H_0:\sigma^2=136.2.$

Alternative hypothesis $H_a:\sigma^2<136.2.$

Tests statistic: $\chi^2=\frac{(n-1)s^2}{\sigma^2}=\frac{(8-1)*115.1}{136.2)}=5.92.$

Degrees of freedom: $df=n-1=8-1=7.$

P-value: $p=P(\chi^2<5.92)=$ 0.4509.

Since the p-value is greater than 0.01, fail to reject the null hypothesis.

There is no sufficient evidence that the recent variance for number of mountain-climber deaths is less than 136.2.