Rising prescription drug prices caused the U.S. Congress to consider laws that would force pharmaceutical companies to offer prescription discounts to senior citizens without drug benefits. The House Government Reform Committee provided data on the prescription cost of some of the most widely used drugs (Newsweek, May 8, 2000). Assume the following data show a sample of the prescription cost in dollars for Zocor®, a drug used to lower cholesterol: 110, 112, 115, 99, 100, 98, 104, 126. Assuming a normal population distribution, what is the 95% confidence interval estimate of the population mean cost for a prescription of Zocor®? _____________________

To calculate the 95% confidence interval estimate of the population mean cost for a prescription of Zocor®, you can use the following steps:

Step 1: Calculate the sample mean (x̄) and sample standard deviation (s) from the given data.
- Add up all the values: 110 + 112 + 115 + 99 + 100 + 98 + 104 + 126 = 864
- Divide the sum by the number of values (n): 864 / 8 = 108 (x̄)
- Calculate the sample standard deviation (s) using the formula:
s = sqrt(∑(x - x̄)² / (n - 1))
= sqrt((110 - 108)² + (112 - 108)² + (115 - 108)² + (99 - 108)² + (100 - 108)² + (98 - 108)² + (104 - 108)² + (126 - 108)² / (8 - 1))
= sqrt(826 / 7)
≈ 6.08

Step 2: Determine the critical value corresponding to a 95% confidence level.
Since we assume a normal population distribution, we can use a t-distribution. With a sample size of 8 (n = 8), the degrees of freedom (df) are (n - 1) = 7. Looking up the critical value for a 95% confidence level and 7 degrees of freedom in the t-table, we find it to be approximately 2.365.

Step 3: Calculate the margin of error (E).
The margin of error represents the range around the sample mean within which we estimate the population mean to fall. It is calculated using the formula:
E = t * (s / sqrt(n))
= 2.365 * (6.08 / sqrt(8))
≈ 5.31

Step 4: Determine the confidence interval.
The confidence interval estimate is calculated by taking the sample mean (x̄) and subtracting the margin of error (E) to get the lower bound (x̄ - E), and adding the margin of error to get the upper bound (x̄ + E).
Lower bound = x̄ - E = 108 - 5.31 ≈ 102.69
Upper bound = x̄ + E = 108 + 5.31 ≈ 113.31

Therefore, the 95% confidence interval estimate of the population mean cost for a prescription of Zocor® is approximately $102.69 to $113.31.

To calculate the 95% confidence interval estimate of the population mean cost for a prescription of Zocor®, we can use the sample data provided.

Step 1: Calculate the sample mean (x̄) and sample standard deviation (s).

Sample mean (x̄) = (110 + 112 + 115 + 99 + 100 + 98 + 104 + 126) / 8 = 105.375
Sample standard deviation (s) = sqrt(((110-105.375)^2 + (112-105.375)^2 + (115-105.375)^2 + (99-105.375)^2 + (100-105.375)^2 + (98-105.375)^2 + (104-105.375)^2 + (126-105.375)^2) / (8-1)) = 8.402

Step 2: Determine the critical value (z) for a 95% confidence level. Since the population distribution is assumed to be normal, we can use the standard normal distribution table or calculator. For a 95% confidence level, the critical value (z) is approximately 1.96.

Step 3: Calculate the margin of error (E).
Margin of error (E) = z * (s / sqrt(n))
where n is the sample size.

Using the provided sample data:

Margin of error (E) = 1.96 * (8.402 / sqrt(8)) = 5.889

Step 4: Construct the confidence interval.
Confidence Interval = x̄ ± E

Substituting the values:

Confidence Interval = 105.375 ± 5.889

Therefore, the 95% confidence interval estimate of the population mean cost for a prescription of Zocor® is approximately (99.486, 111.264).