The following problem is based on information taken from Accidents in North Amer

Question

The following problem is based on information taken from Accidents in North American Mountaineering. Let x represent the number of mountain climbers killed each year. The long-term variation of x is o=12. Suppose that for a random sample of 8 out of the past 15 years, the standard deviation of x has been 10.7. It is known that the population distribution of number of mountain climbers killed each year have a normal distribution.

At a 1% significance level, do the data provide sufficient evidence to claim that the recent variation of mountain-climber deaths is less than o=12?

a) Determine null and alternate hypothesis

b) What is the level of significance?

c) Show that assumptions are met

d) If the p-value is 0.4117, show how you determine if Ho is rejected or not

e) Write the interpretation of the results of the hypothesis test

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   >=   12  
Ha:    sigma   <   12   [ANSWER]

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b)

alpha = 0.01, as given. [ANSWER]

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c)

To use the chi^2 test, we have to have a normally distributed sample from a normally distributed population.

The problem says "It is known that the population distribution of number of mountain climbers killed each year have a normal distribution."

So, it is satisfied.

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d)

As P = 0.4117 > 0.01, we fail to reject Ho. [ANSWER]

[We reject Ho if P < 0.01, and fail to reject otherwise.]

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e)
          
Thus, there is no significant evidence that the recent variation of mountain-climber deaths is less than o=12. [ANSWER]

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