Question

A polling organization asked a nation-wide random sample of 1600 new brides (those who got married in the past 2 years) the following question: "How much money did your wedding cost?" The sample average was about $20,000 with a SD of about $5,000. What most closely resembles the relevant box model? Incorrect It has 1600 tickets marked with "0"s and "1"s. Correct: It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively. Incorrect It has millions of tickets. The average of the tickets is exactly $20,000 and the SD is exactly $5,000. Incorrect It has millions of tickets marked with "0"s and "1"s, but the exact percentage of each is unknown.

Answer 1

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

Explanation:

Given that:

sample size n = 1600

sample mean
`\overline x` = 20000

standard deviation = 5000

The objective is to choose from the given option about what most closely resembles the relevant box model.

The correct answer is:

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

However, if draws are made without replacement, the best estimate of the average amount for the bride will be $20,000

Similarly, the standard error for the sample mean =
`(s)/(√(n))`

`= (5000)/(√(1600))`

`= (5000)/(40)}`

the standard error for the sample mean = 125