Evaluate $E = z^{} \sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}$ for $z^{} = 1.39, σ_{1} = 0.75, σ_{2} = 0.71, n_{1} = 15$ , and $n_{2} = 42$ .
$E = ◻$ (Round to two decimal places as needed.)

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Answer

Rounding to two decimal places, we get the final answer as $E = 0.31$

Steps

Step 1 ：Given values are $z^{*} = 1.39, σ_{1} = 0.75, σ_{2} = 0.71, n_{1} = 15$ , and $n_{2} = 42$

Step 2 ：Substitute the given values into the expression $E = z^{*} \sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}$

Step 3 ：After calculation, we get $E = 0.30926291442411136$

Step 4 ：Rounding to two decimal places, we get the final answer as $E = 0.31$