contestada

Two random samples with sizes 100 and n are chosen from the populations with the means 85.6 and 82.1. They have standard deviations 12.4 and 8.9, respectively. Which of these values of n would result in the smallest SE?

a. 100
b. 120
c. 90
d. 50
e. 70

Respuesta :

Answer:

[tex] SE= \sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}[/tex]

And for this case if we have the same sample size we got the minimum value when we have the higher value fo n for each one and for this case would be the answer:

b. 120

Step-by-step explanation:

For this case we have the following info given:

[tex] n_1 = n_2 = 100[/tex]

[tex]\mu_1 = 85.6[/tex]

[tex]\mu_2 = 82.1[/tex]

[tex] \sigma_1 =12.4[/tex]

[tex]\sigma_2 = 8.9[/tex]

We assume that the variable of interest is the linear combination of the two means and for this case the standard error would be given by:

[tex] SE= \sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}[/tex]

And for this case if we have the same sample size we got the minimum value when we have the higher value fo n for each one and for this case would be the answer:

b. 120

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