Question

In a survey, 19 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 of $18. Construct a confidence interval at a 80% confidence level.

Give your answers to one decimal place.

Answer 1

To construct a confidence interval at an 80% confidence level given a mean of $44, standard deviation of $18, and a sample size of 19, we can use the formula: Confidence interval = mean ± (critical value) × (standard deviation / square root of sample size). By plugging in the values, we can calculate that the confidence interval is approximately (35.7, 52.3).

Step-by-step explanation:

To construct a confidence interval at an 80% confidence level, we can use the following formula:

Confidence interval = mean ± (critical value) × (standard deviation / square root of sample size)

First, we need to find the critical value for an 80% confidence level. Looking up the value in the z-table, we find that the critical value is approximately 1.28.

Next, we can plug in the values into the confidence interval formula:

Confidence interval = 44 ± (1.28) × (18 / square root of 19)

Calculating this,

Confidence interval ≈ 44 ± 8.31

Therefore, the confidence interval is approximately (35.7, 52.3) at the 80% confidence level.