Answer to Question #208406 in Statistics and Probability for basit

Question

For a populationof 17 year old boys and 17year old girls, the means and standard deviations, respectively, of their subscapular skinfold thickness values are as fllows : boys, 9.7 and 6.0: girls, 15.6 and 9.5. smple random samples of 40 boys and 35 girls are selected from the populations. What is the probability that the difference between sample means will be greater than 10?

Answer 1

For boys-

Mean $\bar{x_1}=9.7,$

Standard deviation $\sigma_1=6$

$n_1=40$

For girls-

Mean $\bar{x_2}=15.6$

Standard deviation $\sigma_2=9.5$

$n_2=35$

Probability that the difference between sample means will be greater than 10-

$P(x_1-x_2>10)=P(Z>\dfrac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}})\\[9pt]=P(Z>\dfrac{9.7-15.6}{\sqrt{\frac{6^2}{40}+\frac{9.5^2}{35}}})=P(Z>-3.146)=0.9917$