type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction…
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.\nthe standard deviation of a sample taken from population a is 17.6 for a sample of 25. the standard deviation of a sample taken from population b is 21.2 for a sample of 30.\nthe standard deviation of the sample mean differences is \n(round your answer to the nearest hundredth.)
Answer
Answer:
5.01
Explanation:
Step1: Recall the formula
The formula for the standard deviation of the sample - mean differences is $\sigma_{\bar{x}_1-\bar{x}_2}=\sqrt{\frac{\sigma_1^{2}}{n_1}+\frac{\sigma_2^{2}}{n_2}}$.
Step2: Identify the values
We have $\sigma_1 = 17.6$, $n_1 = 25$, $\sigma_2=21.2$, and $n_2 = 30$.
Step3: Calculate $\sigma_1^{2}$ and $\sigma_2^{2}$
$\sigma_1^{2}=(17.6)^{2}=309.76$ and $\sigma_2^{2}=(21.2)^{2}=449.44$.
Step4: Calculate $\frac{\sigma_1^{2}}{n_1}$ and $\frac{\sigma_2^{2}}{n_2}$
$\frac{\sigma_1^{2}}{n_1}=\frac{309.76}{25}=12.3904$ and $\frac{\sigma_2^{2}}{n_2}=\frac{449.44}{30}\approx14.9813$.
Step5: Calculate the sum
$\frac{\sigma_1^{2}}{n_1}+\frac{\sigma_2^{2}}{n_2}=12.3904 + 14.9813=27.3717$.
Step6: Calculate the square - root
$\sigma_{\bar{x}_1-\bar{x}_2}=\sqrt{27.3717}\approx5.01$.