A random sample of clients at a weight loss center were given a dietary supplement to see if it would promote weight loss. The center reported that the 100 clients lost an average of 34 pounds, and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±10 pounds.
What is your question?
Describe one personal score for each type of measurement scale (ratio, interval, ordinal, and ratio). Explain how the personal score relates/related to the appropriate measure of central tendency (mean,mode, median).
Miles per month spent commuting
GPA of several terms
Average amount per month spent on groceries
To calculate the 95% confidence interval for the mean weight loss using the given information, follow these steps:
1. Identify the sample size: The sample size is given as 100 clients.
2. Determine the margin of error: The margin of error is given as ±10 pounds.
3. Calculate the standard error (SE) of the sample mean:
SE = margin of error / (critical value × square root of sample size)
Since the confidence level is 95%, the critical value can be found using a standard normal distribution table. For a 95% confidence level, the critical value (Z) would be 1.96 (approximately).
SE = 10 / (1.96 × square root of 100) = 10 / (1.96 × 10) = 10 / 19.6 = 0.51 pounds (rounded to 2 decimal places)
4. Calculate the lower and upper bounds of the confidence interval:
The lower bound can be found by subtracting the standard error from the sample mean, and the upper bound can be found by adding the standard error to the sample mean.
Lower bound = sample mean - (standard error)
Upper bound = sample mean + (standard error)
Lower bound = 34 - 0.51 = 33.49 pounds (rounded to 2 decimal places)
Upper bound = 34 + 0.51 = 34.51 pounds (rounded to 2 decimal places)
Therefore, the 95% confidence interval for the mean weight loss produced by the dietary supplement is approximately 33.49 pounds to 34.51 pounds.
To calculate the confidence interval for the mean weight loss, we first need to determine the sample mean and the margin of error.
The sample mean weight loss is given as 34 pounds.
The margin of error is ±10 pounds.
To calculate the confidence interval, we add and subtract the margin of error from the sample mean.
Upper limit of confidence interval = sample mean + margin of error
Upper limit = 34 + 10 = 44 pounds
Lower limit of confidence interval = sample mean - margin of error
Lower limit = 34 - 10 = 24 pounds
Therefore, the 95% confidence interval for the mean weight loss produced by the dietary supplement is between 24 pounds and 44 pounds.
This means that if we were to repeatedly take random samples from the population and calculate the confidence intervals, we would expect 95% of those intervals to contain the true population mean weight loss.