Question

In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $48 and standard deviation of $13. Construct a confidence interval at a 99% confidence level.

Answer 1

To construct a confidence interval at a 99% confidence level for the mean amount spent on their child's last birthday gift, use the formula: Confidence Interval = Mean +/- (Critical Value) x (Standard Deviation / sqrt(N)). The critical value for a 99% confidence interval is approximately 2.6.

Step-by-step explanation:

To construct a confidence interval for the mean amount spent on their child's last birthday gift, we can use the formula:

Confidence Interval = Mean +/- (Critical Value) x (Standard Deviation / sqrt(N))

The critical value for a 99% confidence interval is approximately 2.6. So, the confidence interval is $48 +/- 2.6 x ($13 / sqrt(10)).

Calculating the confidence interval:

Lower bound = $48 - 2.6 x ($13 / sqrt(10))

Upper bound = $48 + 2.6 x ($13 / sqrt(10))

Therefore, the confidence interval at a 99% confidence level is approximately $39.77 to $56.23.