Question

The annual salaries​ (in dollars) of 14 randomly chosen fire fighters are listed. At a=0.05​, is there enough evidence to support the claim that the standard deviation of the annual salaries is different from $5400​?

Assume the population is normally distributed. Complete parts​ (a) through​ (e) below.

50,760 40,978 52,376 46,496 41,734 40,201 51,108

52,047 43,817 34,951 35,075 28,241 32,700 37,958

Write the claim mathematically and identify Ho and Ha

Find the critical value x^2o=

Identify the rejection region

Find the standardized test statistic for the x^2 test

Do we reject or fail why

Is there enough or is not enough evidence and why

Answer 1

H₀: σ = 5400 the standard deviation of the annual salaries is equal to $5400​

H₁: σ ≠ 5400 the standard deviation of the annual salaries is different from $5400​

Critical Value = for 13 degrees of freedom and 5% level of significance = 24.74

= 24.74

the rejection region will be the region in chi-square cart after the = 24.74 i.e., if test statistc is more than then hypothesis test will be rejected. the rejection will be (24.74 , infinity)

Standardised test statistic

Where S² = sample variance = 60456301

= 26.95

since > we reject null hypothesis. that means there is statistically sufficient evidence that the standard deviation of the annual salaries is different from $5400​.