3 years ago

Square route of fifty six

Mathematics

1 answer:

TiliK225 [7]3 years ago

6 0

7.48331477355

Hope this helps!

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(CO 4) In a sample of 8 high school students, they spent an average of 24.8 hours each week doing sports with a sample standard

AveGali [126]

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(22.12, 27.48)

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.95=0.05$

Sample size : n= 8 , which is a small sample (n<30), so we use t-test.

Critical values using t-distribution: $t_{n-1,\alpha/2}=t_{7,0.025}=2.365$

Sample mean : $\overline{x}=24.8\text{ hours}$

Standard deviation : $\sigma=3.2\text{ hours}$

The confidence interval for population means is given by :-

$\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

i.e. $24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}$

$24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)$

Hence, the 95% confidence interval, assuming the times are normally distributed.= (22.12, 27.48)

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