Question

Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. An article reported on body composition and metabolic changes for individuals who had taken various antipsychotic drugs for short periods of time. (a) The sample of 41 individuals who had taken aripiprazole had a mean change in total cholesterol (mg/dL) of 3.55, and the estimated standard error sD n was 3.478. Calculate a confidence interval with confidence level approximately 95% for the true average increase in total cholesterol under these circumstances. (Round your answers to two decimal places.)

Answer 1

Answer:

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Step-by-step explanation:

Step(i):-

Given sample size 'n' =41

Mean of the sample(x⁻)  = 3.55

The estimated standard error

                                             $S.E = \frac{S.D}{\sqrt{n} }$

Given  estimated standard error ( S.E) = 3.478

Level of significance ∝=0.05

Step(ii):-

95% for the true average increase in total cholesterol under these circumstances

$(x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)$

Degrees of freedom

ν= n-1 = 41-1 =40

t₀.₀₅ = 1.6839

95% for the true average increase in total cholesterol under these circumstances

$(x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)$

( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )

(3.55 - 5.856 , 3.55 + 5.856)

(-2.306 , 9.406)

Conclusion:-

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)