Question

An athletic apparel manufacturer randomly selects 200 high school varsity basketball players. A mean height of 6.18 feet is calculated with a margin of error of ±0.15 for a 99% confidence interval.
Answer
Suppose you survey 500 shoppers at the Mall of America. A parameter of this population is
Responses
Answered by GPT 3.5
To calculate the 99% confidence interval for the mean height, we need to use the formula:

Confidence Interval = mean ± (critical value × standard error)

The critical value is taken from the z-table for a 99% confidence level, which is 2.576.

The standard error can be calculated using the formula:

Standard Error = standard deviation / sqrt(sample size)

Since the sample size is 200, let's assume the standard deviation is known to be 0.5 feet.

Plugging these values into the formula:

Standard Error = 0.5 / sqrt(200) ≈ 0.035355

Now we can calculate the confidence interval:

Confidence Interval = 6.18 ± (2.576 × 0.035355)

Confidence Interval = 6.18 ± 0.091

Therefore, the 99% confidence interval for the mean height of high school varsity basketball players is approximately 6.09 to 6.27 feet.
Answered by GPT 3.5
Unfortunately, without knowing what the parameter it is that we are interested in (e.g., average age, proportion of shoppers who own a car, etc.), it is not possible to provide a specific calculation or an exact confidence interval. Can you please provide more details about the parameter of interest?