Question

In: Statistics and Probability

A pharmaceutical company operates retail pharmacies in 10 eastern states.​ Recently, the​ company's internal audit department...

A pharmaceutical company operates retail pharmacies in 10 eastern states.​ Recently, the​ company's internal audit department selected a random sample of​ n=

300300

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 overbarxequals=​$14.5714.57

and

sequals=4.504.50.

Complete parts a and b below.

a. The​ 90% confidence interval estimate for the true average sales value for prescriptions issued by the company is from  

​$14.1414.14   

to    

​$14.9914.99.

​(Round to the nearest​ cent- 2 decimal places. Use ascending​ order.)

You are asked to interpret the meaning of this confidence interval by choosing the correct answer​ below:

A.

The company believes with​ 90% confidence that the true mean prescription amount is between these two amounts.

Your answer is correct.

B.

The company believes with​ 90% confidence that the sample mean prescription amount is between these two amounts.

C.

There is a 0.90 probability that the true mean prescription amount is between these two values.

D.

The company believes that the true mean prescription amount falls between these two values​ 90% of the time.

b. One of its retail outlets recently reported that it had monthly revenue of

​$7 comma 5047,504

from

526526

prescriptions. Are such results to be​ expected? Should that retail outlet be​ audited?

​(Round to the nearest cent as​ needed.)

When the population mean is at the upper limit of the​ 90% confidence interval computed in part​ a, the upper limit of the​ 90% confidence interval for the expected total monthly revenue for

526526

prescriptions would be

​$7,889.307,889.30.

When the population mean is at the lower limit of the​ 90% confidence interval computed in part​ a, the lower limit of the​ 90% confidence interval for the expected total monthly revenue for

526526

prescriptions would be

​$7,438.347,438.34.

Since this outlet reported sales of

​$7 comma 5047,504

from

526526

​prescriptions, there is

no

reason to believe that this is out of line. The retail outlet

should not

be audited.

Solutions

Expert Solution

A pharmaceutical company operates retail pharmacies in 10 eastern states.​ Recently, the​ company's internal audit department selected a random sample of​ n=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

xbar=​$14.57

and

s=4.50.

a. The​ 90% confidence interval estimate for the true average sales value for prescriptions issued by the company is from $14.14 to $14.99.

Answer:-

A. The company believes with​ 90% confidence that the true mean prescription amount is between these two amounts.

b.

b. One of its retail outlets recently reported that it had a monthly revenue of ​$7,504 from 526 prescriptions.

Are such results to be​ expected? Should that retail outlet be​ audited?

The confidence interval is $14.14 to $14.99.

( $ 14.14 * 526 , $ 14.99 * 526 )

= ( $7437.64, $ 7884.74)

The confidence interval is ( $7437.64, $ 7884.74)

therefore $ 7504 is lies in the confidence interval .

So such result is expected.No need to audit the retail

Answer:- Since this outlet reported sales of $7504 from 526 prescriptions,

there is no reason to believe that this is out of line.

The retail outlet should not be audited.

orchestra answered 2 years ago
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