Question

In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $44 and standard deviation (s) of $2. Construct a confidence interval at a 95% confidence level.

Answer 1

To construct a 95% confidence interval for the money spent on a child's last birthday gift from a sample, find the critical t-value based on 25 degrees of freedom, calculate the margin of error using the sample standard deviation and the sample size, and apply this margin to the mean to find the range.

Step-by-step explanation:

To construct a 95% confidence interval for the amount spent on a child's last birthday gift, given a sample mean of $44 and a standard deviation of $2 from 26 people, we will use the t-distribution since the sample size is less than 30 and the standard deviation is a sample standard deviation, not the population standard deviation.

First, identify the critical t-value that corresponds to a 95% confidence level for a sample size of 26, which gives us 25 degrees of freedom (df = n - 1).

Next, calculate the margin of error (ME) using the following formula:

ME = t * (s / √n)

Where:

• t is the critical t-value
• s is the sample standard deviation
• n is the sample size

After finding the margin of error, construct the confidence interval:

Confidence interval = mean ± ME

This range will provide the interval in which we can be 95% confident that the population mean lies.