Question

in a survey, 28 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $49 and standard deviation of $18. estimate how much a typical parent would spend on their child's birthday gift (use a 80% confidence level).

Answer 1

To estimate how much a typical parent would spend on their child's birthday gift, we can use the concept of confidence intervals. The 80% confidence interval for the typical amount a parent would spend on their child's birthday gift is approximately $41.34 to $56.66.

Step-by-step explanation:

To estimate how much a typical parent would spend on their child's birthday gift, we can use the concept of confidence intervals. Since the sample mean is $49 and the standard deviation is $18, we can calculate the 80% confidence interval using the formula:

Confidence Interval = Mean ± (Critical value) × (Standard deviation / √(Sample size))

For an 80% confidence level, the critical value is approximately 1.282. Plugging the values into the formula:

Confidence Interval = $49 ± (1.282) × ($18 / √(28))

Simplifying the expression:

Confidence Interval = $49 ± $7.66

Therefore, the 80% confidence interval for the typical amount a parent would spend on their child's birthday gift is approximately $41.34 to $56.66.