Question

In: Statistics and Probability

A meteorologist states that the standard deviation of the number of deaths annually from volcanoes in...

A meteorologist states that the standard deviation of the number of deaths annually from volcanoes in Hawaii is greater than 36. If a random sample of 16 years had a standard deviation of 40, is the claim believable? Use a=0.1

Expert Solution

Solution:

Given:

Claim: the standard deviation of the number of deaths annually from volcanoes in Hawaii is greater than 36.

that is:

Sample size = n = 16

Sample standard deviation = s = 40

Level of significance = 0.1

Step 1) State H0 and H1:

Vs

this is right tailed test ( > )

Step 2) Test statistic:

Step 3) Find Chi-square critical value:

df = k - 1 = 16 -1 = 15

Level of significance = 0.10

Chi-square critical value = 22.307

Step 4) Decision Rule:

Reject null hypothesis H0, if Chi square test statistic > Chi-square critical value =22.307, otherwise we fail to reject H0.
Since Chi square test statistic = < Chi-square critical value =22.307, we fail to reject H0.

Step 5) Conclusion:

At 0.10 level of significance , there is not sufficient evidence to support the claim that the standard deviation of the number of deaths annually from volcanoes in Hawaii is greater than 36.

orchestra answered 2 years ago

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