In a survey, 16 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 and standard deviation of $4. Construct a confidence intérval at a $80% confidence level.
Give your answers to one decimal place.

Step 1 ：In a survey, 16 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 and standard deviation of $4. We are asked to construct a confidence interval at a 80% confidence level.

Step 2 ：To construct a confidence interval, we need to use the formula: \[\text{Confidence Interval} = \text{mean} \pm Z \times \frac{\text{standard deviation}}{\sqrt{\text{sample size}}}\] where Z is the Z-score corresponding to the desired confidence level.

Step 3 ：For a 80% confidence level, the Z-score is approximately 1.28. This value can be found in a standard Z-table or calculated using a statistical function.

Step 4 ：We have all the other values we need: the mean (34), the standard deviation (4), and the sample size (16). So we can plug these values into the formula to calculate the confidence interval.

Step 5 ：Substituting the given values into the formula, we get: \[\text{Confidence Interval} = 34 \pm 1.28 \times \frac{4}{\sqrt{16}}\]

Step 6 ：Solving the above expression, we get the confidence interval as (32.7, 35.3).

Step 7 ：Final Answer: The 80% confidence interval for the amount spent on their child's last birthday gift is \(\boxed{(32.7, 35.3)}\).