Question

# Consider the following hypothesis test. H0: μ1 − μ2 ≤ 0 Ha: μ1 − μ2 >...

Consider the following hypothesis test.

H0: μ1 − μ2 ≤ 0

Ha: μ1 − μ2 > 0

The following results are for two independent samples taken from the two populations.

Sample 1 Sample 2

n1 = 40

n2 = 50

x1 = 25.7

x2 = 22.8

σ1 = 5.7

σ2 = 6

(a)

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

(b)

(c)

With

α = 0.05,

what is your hypothesis testing conclusion?

Reject H0. There is sufficient evidence to conclude that μ1 − μ2 > 0. Reject H0. There is insufficient evidence to conclude that μ1 − μ2 > 0.      Do not Reject H0. There is sufficient evidence to conclude that μ1 − μ2 > 0. Do not reject H0. There is insufficient evidence to conclude that μ1 − μ2 > 0.

a) test statistic

Z = (x1bar - x2bar)/sqrt [ 12/n1 + 22/n2 ]

Z = ( 25.7 -22.8)/sqrt[ 5.72/40 + 62/50]

Z = 1.89

b) For Z = 1.89 and right tailed test

p-value = P ( Z > 1.89)

p-value = 0.0294

c) if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

our p-value = 0.0294 < 0.05

Conclusion : Reject Ho  There is sufficient evidence to conclude that μ1 − μ2 > 0

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