Answer:
p-value = 0.02535
Step-by-step explanation:
From the information given:
For men:
The sample size n₁ = 10
The standard deviation s₁ = 0.2
The sample mean [tex]\bar x _1 =[/tex] 2.9
For women:
The sample size n₂ = 10
The standard deviation s₂ = 0.2
The sample mean [tex]\bar x _2=[/tex] 3.1
Using the pooled variance;
[tex]S_i = \sqrt{\dfrac{s^2_1}{n_1} +\dfrac{s^2_2}{n_2} }[/tex]
[tex]= \sqrt{\dfrac{0.2^2}{10} +\dfrac{0.2^2}{10} }[/tex]
[tex]= \sqrt{0.004+0.004 }[/tex]
[tex]= \sqrt{0.008 }[/tex]
= 0.08944
The z-test statistics is computed as:
[tex]z = \dfrac{\barf x_1 - \bar x_2}{S_i}[/tex]
[tex]z = \dfrac{2.9- 3.1}{0.08944}[/tex]
z = - 2.236
The p-value = 2 × P(Z < -2.236)
From the z table;
p-value = 2 × (0.012675)
p-value = 0.02535
