Question

An experimenter would like to construct a 99% two-sided t-interval, with a length at almost 0.2 ohms, for the average resistance of a segment of copper cable of a certain length. If the experimenter feels that the standard deviation of such resistances is no larger than 0.15 ohms, what sample size would you recommend? Assume that an appropriate t-value is 3.0.A. Aprox 10B. Aprox 20C. Aprox 30D. Aprox 40E. Aprox 50

Answer 1

Answer:

Aprox 20

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean

s represent the sample standard deviation

n represent the sample size (variable of interest)

Confidence =99% or 0.99

The margin of error is given by this formula:

$ME=t_{\alpha/2}\frac{s}{\sqrt{n}}$    (1)

And on this case we have that ME =0.2/2=0.1 ohms, since the lenght of the confidence interval is L=2ME and we are interested in order to find the value of n, if we solve n from equation (4) we got:

$n=(\frac{t_{\alpha/2} s}{ME})^2$   (2)

The critical value for 99% of confidence interval is provided, $t_{\alpha/2}=3.0$, replacing into formula (2) we got:

$n=(\frac{3.0(0.15)}{0.1})^2 =20.25 \approx 21$

So the answer for this case would be n=21 rounded up to the nearest integer

And with the options provided the best answer is:

Aprox 20