Mathematics: The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval

I think it s 2.5(I don t want to sound to sure, but I took the test and I know it s not 5.0)...

The difference between teenage female and male depression

eboniwiley

30.01.2022

The 95% confidence interval is $0.0112 < \mu_m - \mu_f < 0.1288$

Step-by-step explanation:

From the question we are told that

The sample mean difference is $\= x_m - \= x_f = 0.07$

The standard error is SE = 0.03

Given that the confidence interval is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha =0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * SE$

substituting values

E = 1.96 * 0.03

E = 0.0588

The 95% confidence interval is mathematically represented as

$(\= x_m - \= x_f ) - E < \mu_m - \mu_f$

substituting values

$0.07 - 0.0588 < \mu_m - \mu_f$

$0.0112 < \mu_m - \mu_f < 0.1288$

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