The 95% confident that the average amount spent on a child's birthday gift is between $45.23 and $54.37.
To estimate how much a typical parent would spend on their child's birthday gift (using a 95% confidence level), we can use the following formula:
Mean ± Margin of Error
The margin of error can be calculated using the following formula:
Critical Value * Standard Error of the Mean
The critical value can be found using a t-distribution table, with degrees of freedom equal to the sample size minus 1.
In this case, the sample size is 28, so the degrees of freedom are 27.
For a 95% confidence level and 27 degrees of freedom, the critical value is 2.055.
The standard error of the mean is calculated as follows:
Standard Error of the Mean = Standard Deviation / √Sample Size
In this case, the standard deviation is $12.4 and the sample size is 28, so the standard error of the mean is $2.2.
Therefore, the margin of error is:
Critical Value * Standard Error of the Mean = 2.055 * $2.2 = $4.57
The mean amount of money that a parent would spend on their child's birthday gift is $49.8.
Therefore, our estimate of how much a typical parent would spend on their child's birthday gift is: $49.8 ± $4.57
In other words, we can be 95% confident that the average amount spent on a child's birthday gift is between $45.23 and $54.37.