Question

You may need to use the appropriate technology to answer this 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. Assume population variances are unknown and unequal.

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: 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? The degrees of freedom for this test are 87. (Round your answer to four decimal places.)

p-value =

Answer 1

: Average salaries for staff nurses in City A

:  Average salaries for staff nurses in City B

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

i.e   i.e is our alternate hypothesis:

(a)

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ < 0

Left Tailed test;

(b)

value of the test statistic

value of the test statistic = -2.1880

(c)

Given, The degrees of freedom for this test are 87

For Left tailed test :

For 87 degrees of freedom,

p-value = 0.0157

p-value is computed using excel function : T.DIST.RT(-2.188,87) as follows

T.DIST.RT function

Returns the right-tailed Student's t-distribution.

The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.

Syntax

T.DIST.RT(x,deg_freedom)

The T.DIST.RT function syntax has the following arguments:

X     Required. The numeric value at which to evaluate the distribution.

Deg_freedom     Required. An integer indicating the number of degrees of freedom