The following problem is based on information taken from Acc

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

Solution

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]