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

Mean ± 1.96 Z = ?

To calculate the 95% confidence interval estimate of the population mean cost for a prescription of Zocor, we can follow these steps:

Step 1: Calculate the sample mean (x̄) and sample standard deviation (s).
For the given data, the sample mean (x̄) can be calculated by summing up all the values and dividing by the total number of values:
x̄ = (110 + 112 + 115 + 99 + 100 + 98 + 104 + 126) / 8
x̄ = 864 / 8
x̄ = 108

Next, we calculate the sample standard deviation (s). The formula to calculate the sample standard deviation is as follows:
s = √[Σ(xᵢ - x̄)² / (n - 1)]

First, calculate the squared deviation for each value by subtracting the mean from each value and squaring the result:
(110 - 108)² = 4
(112 - 108)² = 16
(115 - 108)² = 49
(99 - 108)² = 81
(100 - 108)² = 64
(98 - 108)² = 100
(104 - 108)² = 16
(126 - 108)² = 324

Now, sum up all the squared deviations:
Σ(xᵢ - x̄)² = 4 + 16 + 49 + 81 + 64 + 100 + 16 + 324 = 654

Finally, divide the sum of squared deviations by (n - 1) and take the square root:
s = √(654 / (8-1))
s = √(654 / 7)
s ≈ √93.43
s ≈ 9.664

Step 2: Calculate the margin of error (E).
The margin of error (E) can be calculated using the formula:
E = t * (s/√n)

Here, we need to find the t-value for a 95% confidence level. Since our sample size is small (n < 30), we use a t-distribution instead of a z-distribution. For a 95% confidence level with 8 degrees of freedom, the t-value can be obtained from a t-table or calculator.
For our sample size (n = 8), the t-value is approximately 2.36.

Plugging in the values, we get:
E = 2.36 * (9.664/√8)
E ≈ 2.36 * (9.664/2.828)
E ≈ 2.36 * 3.424
E ≈ 8.078

Step 3: Calculate the confidence interval.
The confidence interval is given by the formula:
CI = x̄ ± E

Plugging in the values, we get:
CI = 108 ± 8.078
CI ≈ (108 - 8.078, 108 + 8.078)
CI ≈ (99.922, 116.078)

Therefore, the 95% confidence interval estimate of the population mean cost for a prescription of Zocor is approximately $99.92 to $116.08.