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:

Find the

Assume normal populations, with equal variances.

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:

Find the

Assume normal populations, with equal variances.

You can still ask an expert for help

Nannie Mack

Answered 2021-08-07
Author has **1** answers

Step 1

Given data:

${n}_{1}=13$ ,

${\stackrel{\u2015}{x}}_{1}=20$

${\sigma}_{1}^{2}=1$ ,

${\sigma}_{1}=1$

${n}_{2}=16$ ,

${\stackrel{\u2015}{x}}_{2}=15$ ,

${\sigma}_{2}^{2}=1.8$

${\sigma}_{2}=1.34$

Confidence level$=99\mathrm{\%}$

The formula for confidence interval is:

$C.I.=\stackrel{\u2015}{X}\pm Z\times \frac{\sigma}{\sqrt{n}}$

For the sample 1:

Put the values for sample 1:

$C.I.=\stackrel{\u2015}{X}\pm Z\times \frac{\sigma}{\sqrt{n}}$

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

$C.I.=20\pm 0.714$

$C.I.=[19.28-2.71]$

Step 2

For sample 2 the CI is:

$C.I.=\stackrel{\u2015}{X}\pm Z\times \frac{\sigma}{\sqrt{n}}$

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

$C.I.=15\pm 0.863$

$C.I.=[14.14-15.86]$

For$\mu}_{1}-{\mu}_{2$ :

${\mu}_{1}-{\mu}_{2}={\stackrel{\u2015}{X}}_{1}-{\stackrel{\u2015}{X}}_{2}\pm Z\left(\sqrt{\frac{{\sigma}_{1}^{2}}{{n}_{1}}-\frac{{\sigma}_{2}^{2}}{{n}_{2}}}\right)$

${\mu}_{1}-{\mu}_{2}=20-15\pm 2.77\left(0.45\right)$

${\mu}_{1}-{\mu}_{2}=5\pm 1.24$

${\mu}_{1}-{\mu}_{2}=[3.76-6.24]$

Given data:

Confidence level

The formula for confidence interval is:

For the sample 1:

Put the values for sample 1:

Step 2

For sample 2 the CI is:

For

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