Question

Consider the following hypothesis test.

H_{0}: μ_{1} − μ_{2} ≤ 0

H_{a}: μ_{1} − μ_{2} > 0

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

Sample 1 | Sample 2 |
---|---|

n |
n |

x |
x |

σ |
σ |

(a)

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

(b)

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

(c)

With

α = 0.05,

what is your hypothesis testing conclusion?

Reject *H*_{0}. There is sufficient evidence to
conclude that μ_{1} − μ_{2} > 0. Reject
*H*_{0}. There is insufficient evidence to conclude
that μ_{1} − μ_{2} >
0. Do not Reject
*H*_{0}. There is sufficient evidence to conclude
that μ_{1} − μ_{2} > 0. Do not reject
*H*_{0}. There is insufficient evidence to conclude
that μ_{1} − μ_{2} > 0.

Answer #1

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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x1 = 104
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