Respuesta :
Answer:
= ( 1.39, 2.80) blood level for male is greater than female worker by a figure within confidence interval.
Step-by-step explanation:
From the data given:
[tex]n_1 =152[/tex]
[tex]\bar{x_1} = 5.4 se_1 = 0.3[/tex]
[tex]n_2 = 86 \bar{x_2} = 3.1 se_2 = 0.2[/tex]
Difference between average blood lead levels for male and female is calculated as
[tex]\bar{x_1} -\bar{x_2} = 5.4 - 3.1 = 2.1[/tex]
standard deviation for men is
[tex]s_1 = se_1 \sqrt{n_1}[/tex]
[tex]= 0.3\times \sqrt{152} = 3.70[/tex]
standard deviation for women is
[tex]s_2 = se_2 \sqrt{n_2}[/tex]
[tex]= 0.2\times \sqrt{86} = 1.85[/tex]
The degree of freedom calculated as
[tex]df = n_1 +n_2 -2[/tex]
= 152+86-2 = 236
The t critical value for alpha 0.05 and 236 degree of freedom is 1.97
[tex]CI = \bar{x_1} -\bar{x_2} \pm t_{cr} \sqrt{\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}}[/tex]
[tex]= 2.1 \pm 1.97 \sqrt{\frac{3.70^2}{152}+ \frac{1.58^2}{86}}[/tex]
= ( 1.39, 2.80)
