Mathematics: Construct a 95% confidence interval for the population mean, μ. assume the population has a normal distribution. a random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours

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Construct a 95% confidence interval for the population

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ToriChristine

16.03.2022

Mathematics

$(628.48,\ 661.52)$

Step-by-step explanation:

Given : Sample size : n=16 , which is a small sample (, 30) so we use t-test.

Sample mean : $\overline{x}=645 \text{ hours}$

Standard deviation : $\sigma = 31 \text{ hours}$

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

Critical value : $t_{n-1,\alpha/2}=2.131$

The confidence interval for population mean is given by :-

$\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm(2.131)\dfrac{31}{\sqrt{16}}\\\\\approx645\pm16.52\\\\=(645-16.52,\ 645+16.52)\\\\=(628.48,\ 661.52)$

Hence, a 95% confidence interval for the population mean $\mu$ = $(628.48,\ 661.52)$

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Construct a 95% confidence interval for the population mean, μ. assume the population has a normal distribution. a random sample of 16 lithium batteries has a mean life of 645 hours with a standard deviation of 31 hours

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