# Question

You are evaluating the feasibility of opening a new 10- screen movie theater in a town that has only one existing theater. To be viable, the proposed theater would need an average attendance of at least 15,000 patrons per month. The theater would show movies every day; each of the 10 screens would have a capacity of 120 patrons. An average month has the following characteristics with respect to potential patrons:

Weekdays: 21 days with a total of 20 shows per day (2 show times 3 10 screens)

Weekends: 9 days with a total of 40 shows per day (4 show times 3 10 screens)

Because the current theater maintains no records, you must physically visit the theater and count patrons.

Required:

a. What are some possible methods you can use to estimate the number of patrons on the evenings you visit?

b. What are some precautions that you should consider to ensure a representative sample?

c. What are two possible types of sampling risk that are present in this context? Which of these risks is of more concern to you?

d. Assume that your sampling procedure was employed to provide you 95 percent confidence. How would you react to the following independent outcomes (each sample estimate and precision represents an estimate of the number of patrons per day)?

1. Sample estimate of 600 patrons, precision of 30 patrons.

2. Sample estimate of 680 patrons, precision of 150 patrons.

3. Sample estimate of 490 patrons, precision of 35 patrons.

Weekdays: 21 days with a total of 20 shows per day (2 show times 3 10 screens)

Weekends: 9 days with a total of 40 shows per day (4 show times 3 10 screens)

Because the current theater maintains no records, you must physically visit the theater and count patrons.

Required:

a. What are some possible methods you can use to estimate the number of patrons on the evenings you visit?

b. What are some precautions that you should consider to ensure a representative sample?

c. What are two possible types of sampling risk that are present in this context? Which of these risks is of more concern to you?

d. Assume that your sampling procedure was employed to provide you 95 percent confidence. How would you react to the following independent outcomes (each sample estimate and precision represents an estimate of the number of patrons per day)?

1. Sample estimate of 600 patrons, precision of 30 patrons.

2. Sample estimate of 680 patrons, precision of 150 patrons.

3. Sample estimate of 490 patrons, precision of 35 patrons.

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