The following problem is based on information taken from Accidents in North American Mountaineering (jointly published by The American Alpine Club and The Alpine Club of Canada). Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately s² = 136.2. Suppose that for the past 8 years, the variance has been s² = 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. Find a 90% con­fidence interval for the population variance.

Please provide the following information.

(a) What is the level of signi­ficance? State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. What are the degrees of freedom? What assumptions are you making about the original distribution?

(c) Find or estimate the P-value of the sample test statistic.

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

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

(f) Find the requested confi­dence interval for the population variance or population standard deviation. Interpret the results in the context of the application.