Question

Are nursing salaries in City A lower than those in City B? As reported by a newspaper, salary data show staff nurses in City A earn less than staff nurses in City B. Suppose that in a follow-up study of 40 staff nurses in City A and 50 staff nurses in City B you obtain the following results.

City A	City B
n1 = 40	n2 = 50
x1 = $56,200	x2 = $59,400
s1 = $6,000	s2 = $7,000

(a)

Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that salaries for staff nurses in City A are significantly lower than for those in City B. Use

α = 0.05.

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

    

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ > 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

(b)

What is the value of the test statistic? (Round your answer to three decimal places.)

(c)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Answer 1

The null and alternative hypotheses are,

H0: μ1 − μ2 ≥ 0

Ha: μ1 − μ2 < 0

Using TI-84 calculator we get,

Test statistic is t = -2.334

p-value = 0.0109

Since, p-value = 0.0109 < α = 0.05

We reject the null hypothesis ( H₀ ).