Question

You want to construct a confidence interval for the mean hours of sleep for all college students and you want to find the appropriate sample size for some constraints outlined below. Assume you know the population standard deviation (σ) is 1.45 hours.

(a) Estimate the sample size required to be 95% confident that the sample mean is within 0.2 hours of the population mean for college students.

The minimum sample size is ___ students.

(b) Estimate the sample size required to be 95% confident that the sample mean is within 0.1 hours of the population mean for college students.

The minimum sample size is ____ students.

(c) Estimate the sample size required to be 99% confident that the sample mean is within 0.1 hours of the population mean for college students.

The minimum sample size is ___ students.

Answer 1

Solution :

Given that,

(a)

standard deviation = = 1.45

margin of error = E = 0.2

   Z_/2 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 1.45 ) / 0.2)²

= 202

The minimum sample size is 202 students

(b)

standard deviation = = 1.45

margin of error = E = 0.1

   Z_/2 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 1.45) / 0.1)²

= 808

The minimum sample size is 808 students

(c)

standard deviation = = 1.45

margin of error = E = 0.1

   Z_/2 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 1.45) / 0.1)²

= 1395

The minimum sample size is 1395 students