Question

7. The government conducts a study of the spatial perception among commercial aircrafts pilots. A new test of commercial perceptions is developed, and we want to estimate the mean score for all pilots. How many randomly selected pilots must be tested if we want the sample mean to be in error by no more than 3 points, with a 98% confidence? A preliminary study suggests that the population standard deviation is 24 points.

​​​​​​​Please show hand written work for everything including formulas etc.

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 24

Margin of error = E = 3

At 98% confidence level the z is,

$\alpha$ = 1 - 98%

$\alpha$ = 1 - 0.98 = 0.02

$\alpha$/2 = 0.01

Z_$\alpha$/2 = 2.326

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [2.326 * 24 / 3 ]²

n = 346.25

Sample size = n = 347