Question

changes saved3. In a survey taken in July of 1985, of the 50 households randomly surveyed from across the United States, the proportion of households having apersonal computer was determined to be 11%. The U.S. government census data taken in August 1985 suggested that 11.7% of households in theUnited States had a personal computer. Which statement(s) below support the small discrepancy between the sample proportion of householdshaving a personal computer in July 1985 and the population proportion of households having a personal computer in August 1985?Statement I: The sample size was too small.Statement II: The sample was not truly random.Statement III: The data from July 1985 to August 1985 will have changed substantially.Statement IV: The sample statistic is nearly equal to the population parameter, and will never be exactly equal.Statements I, II, III support the discrepancyStatements I and III only support the discrepancyStatements I and IV only support the discrepancyStatement IV only supports the discrepancy

Answer 1

Errors in statistical data can occur in two forms:

1) Sampling error, which arises when only a part of the population is used to represent the whole population

2) Non-sampling error which can occur at any stage of a sample survey and can also occur with censuses.

The original survey samples 50 households and got a proportion of 11% while the subsequent census gave a relatively accurate proportion of 11.7%.

The difference is slight, just 0.7%.

Let us consider each statement individually to see which could be responsible for the discrepancy.

Statement 1:

A larger sample size usually means that the sampling error decreases and vice-versa. The sample size of 50 households nationwide represents a very small sample size and this could be a reason for the discrepancy.

Therefore, this statement SUPPORTS the discrepancy.

Statement 2:

There is not enough information that supports this statement. If the sample was not truly random, the discrepancies would be non-existent.

Therefore, this statement DOES NOT SUPPORT the discrepancy.

Statement 3:

The difference between the time when the survey and census are taken is just ONE MONTH. This is too short a time for the data to drastically change unless the general populace goes on a sudden month-long PC purge!

Therefore, this statement DOES NOT SUPPORT the discrepancy.

Statement 4:

The difference between both proportions is just 0.7%. This is not a particularly big difference.