Mathematics: John runs 9 miles in an hour. How much distance (in miles) will he cover in 4/3 hours?

John runs 9 miles in an hour. How much distance (in

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27.11.2022

$54.6-3.51\frac{9.2}{\sqrt{48}}=49.94$

$54.6+3.51\frac{9.2}{\sqrt{48}}=59.26$

The confidence interval is given by (49.94, 59.26)

Step-by-step explanation:

Info given

$\bar X=54.6$ represent the sample mean

$\mu$ population mean (variable of interest)

s=9.2 represent the sample standard deviation

n=48 represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom are given by:

df=n-1=48-1=47

The Confidence is 0.999 or 99.9%, and the significance is $\alpha=0.001$ and $\alpha/2 =0.0005$ , and the critical value would be $t_{\alpha/2}=3.51$

And replacing we got:

$54.6-3.51\frac{9.2}{\sqrt{48}}=49.94$

$54.6+3.51\frac{9.2}{\sqrt{48}}=59.26$

The confidence interval is given by (49.94, 59.26)

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