The data, recorded in days, represents the recovery time, for patients who are randomly treated with one of two medications.Find the 99\% confidence interval for \mu1-\mu2, the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs.

Question

The data, recorded in days, represents the recovery time, for patients who are randomly treated with one of two medications.Find the 99\% confidence interval for \mu1-\mu2, the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs.

UkusakazaL 2021-08-03 Answered

The following data, recorded in days, represents the recovery time, for patients who are randomly treated with one of two medications to cure servere bladder infections:
$\begin{array}{cc} M e d i c a t i o n 1 & M e d i c a t i o n 2 \\ n_{1} = 13 & n_{2} = 16 \\ {\bar{x}}_{1} = 20 & {\bar{x}}_{2} = 15 \\ s_{1}^{2} = 2.0 & s_{2}^{2} = 1.8 \end{array}$
Find the $99 %$ confidence interval for $μ 1 - μ 2$ , the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs.
Assume normal populations, with equal variances.

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Expert Answer

Nannie Mack

Answered 2021-08-07 Author has 1 answers

Step 1
Given data:

n_{1} = 13

,

{\overset{―}{x}}_{1} = 20

σ_{1}^{2} = 1

,

σ_{1} = 1

n_{2} = 16

,

{\overset{―}{x}}_{2} = 15

,

σ_{2}^{2} = 1.8

σ_{2} = 1.34

Confidence level

= 99 %

The formula for confidence interval is:

C . I . = \overset{―}{X} \pm Z \times \frac{σ}{\sqrt{n}}

For the sample 1:
Put the values for sample 1:

C . I . = \overset{―}{X} \pm Z \times \frac{σ}{\sqrt{n}}

C . I . = 20 \pm 2.5758 \times \frac{1}{\sqrt{13}}

C . I . = 20 \pm 0.714

C . I . = [19.28 - 2.71]

Step 2
For sample 2 the CI is:

C . I . = \overset{―}{X} \pm Z \times \frac{σ}{\sqrt{n}}

C . I . = 15 \pm 2.5758 \times \frac{1.34}{\sqrt{16}}

C . I . = 15 \pm 0.863

C . I . = [14.14 - 15.86]

For

μ_{1} - μ_{2}

:

μ_{1} - μ_{2} = {\overset{―}{X}}_{1} - {\overset{―}{X}}_{2} \pm Z (\sqrt{\frac{σ_{1}^{2}}{n_{1}} - \frac{σ_{2}^{2}}{n_{2}}})

μ_{1} - μ_{2} = 20 - 15 \pm 2.77 (0.45)

μ_{1} - μ_{2} = 5 \pm 1.24

μ_{1} - μ_{2} = [3.76 - 6.24]

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