Question

In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $34.2 and standard deviation of $2.1. Estimate how much a typical parent would spend on their child's birthday gift (use a 90% confidence level). Give your answers to 3 decimal places. Express your answer in the format of x ˉ ± Error. $±$

Answer 1

A typical parent would spend around $34.20 ± $1.02 on their child's birthday gift.

Step-by-step explanation:

To estimate how much a typical parent would spend on their child's birthday gift with a 90% confidence level, we can use the concept of confidence intervals. The formula for calculating the confidence interval is given by:

X ± (z * (σ/√n))

where X is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

In this case, the sample mean is $34.2, the population standard deviation is $2.1, and the sample size is 13. The z-score for a 90% confidence level is approximately 1.645.

Plugging these values into the formula:

$34.2 ± (1.645 * ($2.1/√13))

Simplifying the formula, we get the confidence interval to be approximately $34.2 ± $1.02.

Therefore, a typical parent would spend around $34.20 ± $1.02 on their child's birthday gift.