A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter?

Question

A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter

of 0.834343 inches with a standard deviation of 0.001886 inches. (a) Why would nickel diameters vary? (b) Construct a 99 percent confidence interval for the true mean diameter of a nickel. (c) Discuss any assumptions that are needed. (d) What sample size would ensure an error of ± 0.0005 inches with 99 percent confidence?

Answer 1

I just had this class, I love statistics.

a) Machines have set tolerances and low tolerances are expensive.  Wear and tear?

b) Mean +/-  error  = confidence interval for the population mean  

   21-1 = 20 degrees of freedom

Error = (t-value) X (0.001886)/(21^0.5)  

look up t-value in table, 0.01 area in two tails   =  2.845

0.834343 - 0.0011709 <x< 0.834343 + 0.0011709

c.  There may be more assumptions but the (numbers?) have to be approximately normal since sample size is below 30.

d.  set error equal to 0.0005 in original equation and solve for n

    0.0005 = 2.845 X [.001886/(n^0.5)]    n=115.22347 or 116

Check my answers for yourself I'm using a computer calculator.

Answer 2

you could at least try a little, like, what did you arrive at?

Answer 3

a) different mints, tools( die and anvil ), temperature at manufacture

and ware

b) null {you do your home work }

c) none { your statistical modleing has a faulty assumption }