Question

Disney's Hannah Montana: The Movie opened in April 2009. The ticket sales revenue ($) for a sample of theaters is below. Use it to answer/do the following. 20,200 8,350 10,750 13,900 13,185 10,150 7,300 6,240 4,200 21,400

(a) Estimate the average ticket sales revenue.

(b) Develop a 90% confidence interval for the mean in (a).

(c) Develop a 95% confidence interval for the mean in (a).

(d) Develop a 99% confidence interval for the mean in (a).

(e) If ticket prices were $7.16 on average, estimate the mean number of customers per theater.

(f) The movie was shown in 3,118 theaters. Estimate the number of people who saw the movie

Answer 1

(a)

Average ticket sales revenue = = 115675/10 = 11567.50

(b)

Sample Standard deviation s = 5707.2932

SE = s/

= 5707.2932/ = 1804.8046

= 0.10

ndf = n - 1 = 10 - 1 = 9

From Table, critical values of t = 1.8331

Confidence interval:

11567.50 (1.8331 X 1804.8046)

= 11567.50 3308.3873

= (8259.11 ,14,875.89)

So,

Confidence Interval:

8259.11 < < 14,875.89

(c)

Sample Standard deviation s = 5707.2932

SE = s/

= 5707.2932/ = 1804.8046

= 0.05

ndf = n - 1 = 10 - 1 = 9

From Table, critical values of t = 2.2622

Confidence interval:

11567.50 (2.2622 X 1804.8046)

= 11567.50 4082.8290

= (7484.67 ,15,650.33)

So,

Confidence Interval:

7484.67 < < 15,650.33

(d)

Sample Standard deviation s = 5707.2932

SE = s/

= 5707.2932/ = 1804.8046

= 0.01

ndf = n - 1 = 10 - 1 = 9

From Table, critical values of t = 3.2499

Confidence interval:

11567.50 (3.2499 X 1804.8046)

= 11567.50 5865.4345

= (5702.07 ,17,432.93)

So,

Confidence Interval:

5702.07 < < 17,432.93

(e)

Mean number of customers per theater = 11,567.50/7.16 = 1615.5726

                                           = 1616 (Round to integer)

So,

Answer is:

1616

(f)

number of people who saw the movie = 1616 X 3118 = 5,037,355

So,

Answer is:

5,037,355