Question

A study is made to determine how much was spent for a product. A sample of 1,000 people was taken. The sample mean was $300 and the sample standard deviation was $90. Calculate: a. the 68.3% confidence interval b. the 95.4% confidence interval c. the 99.7% confidence interval.

Answer 1

To calculate the confidence intervals, use the formula: Confidence Interval = Sample Mean ± (Z * (Sample Standard Deviation / √(Sample Size))). The Z-scores for the different confidence levels can be looked up in a standard normal distribution table.

Step-by-step explanation:

To calculate the confidence interval, we will use the formula:

Confidence Interval = Sample Mean ± (Z * (Sample Standard Deviation / √(Sample Size)))

Where:
- Z is the Z-score corresponding to the desired confidence level.
- Sample Mean is $300.
- Sample Standard Deviation is $90.
- Sample Size is 1,000.

a. For the 68.3% confidence interval, the Z-score is approximately 1.00. Plugging in the values, we get:
Confidence Interval = $300 ± (1.00 * ($90 / √1000))

b. For the 95.4% confidence interval, the Z-score is approximately 1.96. Plugging in the values, we get:
Confidence Interval = $300 ± (1.96 * ($90 / √1000))

c. For the 99.7% confidence interval, the Z-score is approximately 3.00. Plugging in the values, we get:
Confidence Interval = $300 ± (3.00 * ($90 / √1000))