The difference between teenage female and male depression rates estimated from two samples is 0.08. The estimated standard error of the sampling distribution is 0.04. what is the 95% confidence interval? Use the critical value z - 1.96.
Round all calculations to two decimal places. Put lower bound in the first box and upper bound in the second box.

Answer: (0.0016, 0.1584)

Step-by-step explanation:

Given that:

Mean (m) = 0.08

Standard Error = 0.04

Zcritical at 95% = 1.96

Using the relation :

Mean ± Zcritical * (standard error)

0.08 ± 1.96 * (0.04)

Lower boundary = 0.08 - (1.96 * 0.04)

Lower boundary = 0.08 - 0.0784 = 0.0016

Upper boundary = 0.08 + (1.96 * 0.04)

Upper boundary = 0.08 + 0.0784 = 0.1584

Confidence interval is Hence,

(0.0016, 0.1584)

The 95% confidence interval is given by (0.0016 , 0.1584) and this can be evaluated by using the mean and standard error relation.

Given :

To determine the 95% confidence interval using the following relation:

[tex]\rm \mu \pm z_{critical}\times standard \;error[/tex]

[tex]0.08\pm 1.96\times 0.04[/tex]

So, the lower and upper boundary is (0.0016 , 0.1584).

Therefore, the 95% confidence interval is given by (0.0016 , 0.1584).

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