Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

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

Sample 1	Sample 2
n1 = 80	n2 = 70
x1 = 104	x2 = 106
σ1 = 8.2	σ2 = 7.4

(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.)

Answer 1

SOLUTION:

From given data,

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

Sample 1	Sample 2
$n_{1}$ = 80	$n_{2}$ = 70
$x_{1}$ = 104	$x_{2}$ = 106
$\sigma _{1}$ = 8.2	$\sigma _{2}$ = 7.4

The statistical software output for this problem is:

Two sample Z summary hypothesis test:

$\mu _{1}$ : Mean of population 1 (Std. dev. = 8.2)
$\mu _{2}$ : Mean of population 2 (Std. dev. = 7.4)
$\mu _{1}$ - $\mu _{2}$ : Difference between two means
Null hypothesis : H₀ : $\mu _{1}$ - $\mu _{2}$ = 0
Alternative hypothesis : H_a : $\mu _{1}$ - $\mu _{2}$$\neq$ 0

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

Test statistic

z = ($x_{1}$ - $x_{2}$ ) / sqrt ($\sigma_{1}^{2}$ / $n_{1}$ + $\sigma_{2}^{2}$ / $n_{2}$)

z = (104 - 106 ) / sqrt (8.2² / 80 + 7.4² / 70)

z = -2 / 1.273886

z = -1.56

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

p-value

p-value = P (z > -1.56 )

= 1 - P (z < -1.56 )

= 1 - 0.05938

= 0.94062

Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case.