Question

Managers at an automobile manufacturing plant would like to estimate the mean completion time of an assembly line operation, . The managers plan to choose a random sample of completion times and estimate ji via the sample. Assuming that the standard deviation of the population of completion times is 10.3 minutes, what is the minimum sample size needed for the managers to be 95% confident that their estimate is within 2.2 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) x 5 ?

Answer 1

Solution:

Given ,

$\sigma$ = 10.3 ..Population SD

E = 2.2 Margin of error

c = 95% = 0.95 ...confidence level

Find sample size required.

c = 0.95

$\therefore$$\alpha$ = 1- c = 1- 0.95 = 0.05

$\therefore$  $\alpha$/2 = 0.025

Using Z table ,

$\therefore$$Z_{\alpha/2}$ = 1.96

Now, sample size (n) is given by,

40/2 * o n = 13 1 E

=  {(1.96* 10.3 )/ 2.2}2

= 84.2057

= 85 ..(round to the next whole number)

Answer : Required Sample size is n = 85