Exam MAS-I Practice Question 68

Study guide: Exam MAS-I

An insurer's claims department believes its claim sizes follow an exponential distribution with mean 3,000, a figure taken from an industry study. Ten recent claims are:

 $150,\ 250,\ 400,\ 500,\ 650,\ 800,\ 1{,}000,\ 1{,}300,\ 1{,}700,\ 2{,}250$

Use the Kolmogorov–Smirnov critical values 1.22/√n, 1.36/√n and 1.63/√n at the 10%, 5% and 1% significance levels.

Part a (1 point)

Calculate the Kolmogorov–Smirnov statistic $D$ for the hypothesis that the claims are exponential with mean 3,000. Give your answer to three decimal places.

Part b (1 point)

Using your result from part (a), which conclusion follows?

A) Do not reject the exponential model at the 10% level
B) Reject at the 10% level, but not at the 5% level
C) Reject at the 5% level, but not at the 1% level
D) Reject at the 1% level

Part c (1 point)

A second analyst instead sets the exponential mean equal to the sample mean of these ten claims, 900, recomputes the statistic as $D = 0.159$ , compares it with 0.430, and reports that "the exponential model passes at the 5% level." Which assessment of that report is most valid?

A) The report stands: the distribution of $D$ does not depend on the model, so 0.430 still applies
B) The report is unsupported: fitting the mean to these data shrinks $D$ , so 0.430 is too large
C) The report is unsupported: fitting the mean makes $D$ larger, so the test now rejects too often
D) The report stands once the critical value is reduced for one estimated parameter, as in the chi-square test
E) The report stands, and part (b) was the invalid test, because the mean was not estimated from the data

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Exam MAS-I Practice Question 68

Part a (1 point)

Part b (1 point)

Part c (1 point)

Concepts tested

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