Final answer:
To find a 99.8% confidence interval for the mean ideal body weight percentage of diabetics, calculate the sample mean and standard deviation, determine the appropriate t-score, calculate the margin of error, and then establish the interval range around the sample mean.
Step-by-step explanation:
To find a 99.8% confidence interval for the true mean percentage of ideal body weight for the population of insulin-dependent diabetics, we need to follow a series of steps, including calculating the sample mean, the standard deviation, the margin of error, and then using these to determine the interval.
Steps for Calculating the 99.8% Confidence Interval:
- Calculate the sample mean by adding all the percentages and dividing by the number of individuals.
- Compute the sample standard deviation, which measures the spread of weight percentages around the mean.
- Since the sample size is less than 30, we will use the t-distribution. Determine the t-score that corresponds to the 99.8% confidence level.
- Calculate the margin of error by multiplying the t-score by the standard deviation divided by the square root of the sample size.
- Add and subtract the margin of error from the sample mean to obtain the confidence interval.
Keep in mind that the sample mean represents the average ideal body weight percentage, and the confidence interval gives us a range that we are 99.8% certain contains the true population mean of ideal body weight percentages. This calculation is critical for health professionals as it relates to managing type 2 diabetes and the importance of maintaining an ideal body weight for overall health.