UkusakazaL

2021-08-02

A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a

ruigE

Beginner2021-08-10Added 1 answers

Step 1

Solution:

Given information:

$n=125$ Sample size

$x=64.5$ inches Sample mean

$s=5$ inches sample standard deviation

$\alpha =0.05$ Level of significance

Step 2

The 95% confidence interval for the mean is

$\stackrel{\u2015}{x}\pm {t}_{\frac{\alpha}{2},n-1}\times \frac{s}{\sqrt{n}}$

n is large we used$z}_{\frac{\alpha}{2}$ instead of $t}_{\frac{\alpha}{2},n-1$

At$\alpha =0.05$

${z}_{\frac{\alpha}{2}}={z}_{0.05}=1.96$ From Z table

$(64.5\pm 1.96\times \frac{5}{\sqrt{125}})$

$(64.5\pm 1.96\times \frac{5}{11.180339})$

$(64.5\pm 1.96\times 0.4472135)$

$(64.5\pm 0.8765384)$

$(64.5-0.8765384,64.5+0.8765384)$

$(63.62346,65.376538)$

$(63.62,65.38)$

The$95\mathrm{\%}$ confidence interval for the mean is ( 63.62, 65.38)

Solution:

Given information:

Step 2

The 95% confidence interval for the mean is

n is large we used

At

The