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In: Statistics and Probability

Are nursing salaries in City A lower than those in City B? As reported by a...

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 = $56,500

x2 = $59,500

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: μ1μ2 ≠ 0

Ha: μ1μ2 = 0

H0: μ1μ2 ≥ 0

Ha: μ1μ2 < 0

    

H0: μ1μ2 ≤ 0

Ha: μ1μ2 > 0

H0: μ1μ2 > 0

Ha: μ1μ2 = 0

H0: μ1μ2 = 0

Ha: μ1μ2 ≠ 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 =

(d)

What is your conclusion?

Reject H0. There is insufficient evidence to conclude that the salaries of staff nurses are lower in City A than in City B.Do not Reject H0. There is sufficient evidence to conclude that the salaries of staff nurses are lower in City A than in City B.     Reject H0. There is sufficient evidence to conclude that the salaries of staff nurses are lower in City A than in City B.Do not reject H0. There is insufficient evidence to conclude that the salaries of staff nurses are lower in City A than in City B.

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