Question

In recent times, the percent of buyers purchasing a new vehicle via the Internet has been large enough that local automobile dealers are concerned about its impact on their business. The information needed is an estimate of the proportion of purchases via the Internet. How large of a sample of purchasers is necessary for the estimate to be  within 2 percentage points with a 98% level of confidence? Current thinking is that about 8% of the vehicles are purchased via the Internet.

 

 

Answer 1

The estimate of the population proportion is to be within 0.02, so E = 0.02.

The desired level of confidence is 0.98.

Because no estimate of the population proportion is available, we use π = 0.50.

 

Using z-table, at 98% confidence, z = 2.33.

 

Sample size,

n = π(1 – π)(z/E)2

    = 0.50(1 – 0.50)(2.33/0.02)2

   = 3,393.0625

   ≈ 3,394

 

Therefore, we will take a sample of 3,394 purchasers is necessary to know the percent of buyers purchasing a new vehicle via Internet.

 

Given, population proportion, π = 0.08

 

Then the sample is given by

n = π(1 – π)(z/E)2

   = 0.08(1 – 0.08)(2.33/0.02)2

   = 998.9176

   = ≈ 999

 

Therefore, we will take a sample of 999 purchasers is necessary to know the percent of buyers purchasing a new vehicle via Internet.

Therefore, we will take a sample of 999 purchasers is necessary to know the percent of buyers purchasing a new vehicle via Internet.