Question

The admission office wants to estimate the mean age of all students enrolled at ZU. The estimate must be within half year of the population mean. Assume the population of ages is normally distributed.  Also assume that the population standard deviation is 1.4 years.

1- Determine the minimum sample size required to construct a 90% confidence interval for the population mean ?....

2-Repeat part (a) using a 99% confidence interval ? .....

  3-Which level of confidence requires a larger sample size? Explain ....

Answer 1

Solution :

Given that,

standard deviation = = 1.4

margin of error = E = 0.5

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Sample size = n = ((Z/2 * ) / E)2

= ((1.645 * 1.4) / 0.5)2

= 21

Sample size = 21

b ) At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Sample size = n = ((Z/2 * ) / E)2

= ((2.576 * 1.4) / 0.5)2

= 52

Sample size =52

c ) Increasing Confidence level increasing sample size