Respuesta :
Answer:
The 95% confidence interval is [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean difference is [tex]\= x_m - \= x_f = 0.07[/tex]
The standard error is SE = 0.03
Given that the confidence interval is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
substituting values
[tex]E = 1.96 * 0.03[/tex]
[tex]E = 0.0588[/tex]
The 95% confidence interval is mathematically represented as
[tex](\= x_m - \= x_f ) - E < \mu_m - \mu_f <(\= x_m - \= x_f ) + E[/tex]
substituting values
[tex]0.07 - 0.0588 < \mu_m - \mu_f <0.07 + 0.0588[/tex]
[tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
The difference between teenage female and male depression rates are given. The 95% percent confidence interval can be obtained using mean and standard error relation.
The confidence interval is (0.0016 , 0.1584).
Given:
The depression rates is [tex]0.07[/tex].
The standard error of sampling distribution is [tex]0.03[/tex].
The critical value [tex]z=1.96[/tex]
Write the relation for mean and standard error.
[tex]\mu\pm z_{\rm critical}+\rm standard\: error[/tex]
Substitute the value.
[tex]0.07\pm 1.96\times 0.03=(0.1288,\:0.0112)[/tex]
Therefore, the upper and lower boundary is [tex](0.1288,\:0.0112)[/tex]. Thus, The confidence interval is (0.0016 , 0.1584).
Learn more mean and standard error here:
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