Question

A union of truck drivers wants to estimate the proportion of all truckers who suffer from sleep apnea to within plus or minus 2% at the 90% confidence level. Historically, this proportion has been about 7% but there is concern that this may have increased due to the extra stress drivers are under with changes in industry practices. What sample size should the union expect to need?

Answer 1

To estimate the proportion of truckers with sleep apnea at a 90% confidence level within plus or minus 2%, the union needs to survey approximately 906 truckers.

Step-by-step explanation:

To estimate the proportion of all truckers who suffer from sleep apnea within plus or minus 2% at the 90% confidence level, the union needs to determine the sample size.

To calculate the sample size, we can use the formula:

Sample Size = (Zα/2)2 * p * (1 - p) / E2

Where Zα/2 is the Z-value corresponding to the desired confidence level (90% confidence level corresponds to Z0.95 = 1.645), p is the estimated proportion (7% in this case), and E is the desired margin of error (2% in this case).

Plugging in the values, we get:

Sample Size = (1.645)2 * 0.07 * (1 - 0.07) / 0.022

Calculating this, the sample size required is approximately 906 truckers.