Question

A pharmaceutical company operates retail pharmacies in 10 eastern states. Recently, the company's internal audit department selected a random sample of 300 prescriptions issued throughout the system. The objective of the sampling was to estimate the average dollar value of all prescriptions issued by the company. The data collected were x-$14.05 and s 4.00. Complete parts a and b below.

a. Determine the 90% confidence inter al estimate or the true average sales value for presc tions issued by the company Interpret the interval estimate.
The 90% confidence interval is $__________
Interpret the interval. Choose the correct answer below.
A. The company believes with 90% confidence that the sample mean prescription amount is between these two amounts.
B. The company believes that the true mean prescription amount falls between these two values 90% of the time.
C. There is a 0.90 probability that the true mean prescription amount is between these two values.
D. The company believes with 90% confidence that the true mean prescription amount is between these two amounts.

Answer 1

The 90% confidence interval for the true average sales value of prescriptions is approximately ($13.63, $14.47). This interval means that with 90% confidence, the true mean prescription amount is believed to be between these two values. Option d.

Step-by-step explanation:

To calculate the 90% confidence interval for the true average sales value of prescriptions, we use the sample mean (x) of $14.05 and the sample standard deviation (s) of $4.00. Since the sample size is 300, we can use the z-distribution for our calculations.

The formula for a confidence interval is x ± z*(s/√n) where n is the sample size and z is the z-score corresponding to the confidence level. For a 90% confidence level, the z-score is typically 1.645. Plugging in the values, we get 14.05 ± 1.645*(4/√300).

Doing the calculations, the 90% confidence interval is approximately ($13.63, $14.47).

Option D is correct: The company believes with 90% confidence that the true mean prescription amount is between these two amounts. This means that if we were to take many samples and build confidence intervals in the same way, about 90% of those intervals would contain the true population mean.