Question

you randomly select and measure the contents of 10 bottles of cough syrup. the results (in fluid ounces) are shown to the right. 4.218 4.298 4.253 4.242 4.188 4.244 4.265 4.246 4.221 4.236 assume the sample is taken from a normally distributed population. construct 80% confidence intervals for (a) the population variance \\( \sigma^{2} \\) and (b) the population standard deviation \\( \sigma \\). interpret the results. (b) the confidence interval for the population standard deviation is (0.0230, 0.0431). (round to four decimal places as needed.) interpret the results. select the correct choice below and fill in the answer box(es) to complete your choice. (round to four decimal place as needed.) o a. with 80% confidence, you can say that the o b. with 20% confidence, you can say that the population standard deviation is between and population standard deviation is greater than inches. inches. o c. with 20% confidence, you can say that the o d. with 80% confidence, you can say that the population standard deviation is between and population standard deviation is less than inches. inches.

Explanation:

Step1: Understand confidence interval concept

A confidence interval gives a range of values within which the population parameter is likely to lie. An 80% confidence interval for the population standard deviation means that if we were to take many samples and construct confidence intervals in the same way, about 80% of those intervals would contain the true population standard deviation.

Step2: Analyze each option

• Option A: Since the confidence interval for the population standard deviation is (0.0230, 0.0431) and it is an 80% confidence interval, with 80% confidence, we can say that the population standard deviation is between the lower and upper bounds of the interval.
• Option B: The confidence level is 80% for the constructed interval, not 20%. A 20% confidence level is not relevant to the given 80% confidence interval for the standard deviation.
• Option C: The confidence level is 80% for the interval (0.0230, 0.0431), not 20%.
• Option D: The confidence interval is a range (lower - upper), not a one - sided “less than” statement for an 80% confidence interval in this context.

Answer:

A. With 80% confidence, you can say that the population standard deviation is between \(0.0230\) and \(0.0431\) inches.