Question

suppose you wish to estimate a population mean correct to within 0.14 with a confidence level of .90. You do not know σ', but you know that the observations will range in value between 37 and 45. Complete parts a and b. a. Find the approximate sample size that will produce the desired accuracy of the estimate. You wish to be conservative to ensure that the sample size will be ample for achieving the desired accuracy of the estimate. (Hint: assume that the range of the observations will equal 4o.) The approximate sample size is(Round up to the nearest integer) b. Calculate the approximate sample size, making the less conservative assumption that the range of the observations is equal to 6σ The approximate sample size is(Round up to the nearest integer.)

Answer 1

Solution:-

a) The approximate sample size is 553.

M.E = 0.14, C.L = 90%

$4\sigma =45-37$

$4\sigma =8$

$\sigma =2$

$M.E = z_{\alpha /2}\times{\frac{\sigma }{\sqrt{n}}}$

$n = \left (\frac{z_{\alpha /2}\times \sigma }{M.E} \right )^{2}$

$n = \left (\frac{1.645\times 2 }{0.14} \right )^{2}$

n = 552.25

n = 553

b) The approximate sample size is 246.

M.E = 0.14, C.L = 90%

$6\sigma =45-37$

$6\sigma =8$

$\sigma =1.3333$

$M.E = z_{\alpha /2}\times{\frac{\sigma }{\sqrt{n}}}$

$n = \left (\frac{z_{\alpha /2}\times \sigma }{M.E} \right )^{2}$

$n = \left (\frac{1.645\times 1.33333 }{0.14} \right )^{2}$

n = 245.43

n = 246