Question

The annual salaries of 16 randomly chosen actuaries are listed below. At a=0.01 can you conclude that the standard deviation of the annual salaries is greater than $ 20,000 question mark Use the​ P-value method to perform the hypothesis test. 89,480 45,584 58,984 92,296 61,088 40,176 110,016 48,688 103,672 95,992 61,808 46,024 52,944 103,696 55,064 49,568

Answer 1

H₀: = 20000

H₁: > 20000

s = 24678.144

The test statistic = (n - 1)s²/

                                 = 15 * (24678.144)^2/(20000)^2

                                 = 22.84

P-value = P( > 22.84)

             = 0.0876

Since the P-value is greater than the significance level(0.0876 > 0.01), so we should not reject H₀.

At = 0.01, we cannot conclude that the standard deviation of the annual salaries is greater than $20,000.