Question

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by the wall street journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number. A. If we want to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used? assume confidence. B. If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used? assume confidence.

Answer 1

a) The required Sample Size is 40.

b) the required Sample Size is 62.

Step-by-step explanation:

Given the data in the question;

standard deviation σ = 4 minutes

a)

margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes

And 95% confidence.

Now, the Critical Value of z for 0.95 confidence interval;

∝ = 1 - 0.95 = 0.05

= 1.96

so, sample size n will be;

n = [  × σ/E ]²

we substitute;

n = [ 1.96 × (4/1.25) ]²

n =  [ 1.96 × 3.2 ]²

n = [ 6.272 ]²

n = 39.338

Since we referring to a number of samples, it approximately becomes 40

Therefore, the required Sample Size is 40

b)

margin of error E = 1 minutes

And 95% confidence.

Now, the Critical Value of z for 0.95 confidence interval;

∝ = 1 - 0.95 = 0.05

= 1.96

so, sample size n will be;

n = [  × σ/E ]²

we substitute;

n = [ 1.96 × (4/1) ]²

n =  [ 1.96 × 4 ]²

n = [ 7.84 ]²

n = 61.466

Since we referring to a number of samples, its approximately becomes 62.

Therefore, the required Sample Size is 62.

Sample size determination involves choosing the number of observations or repetitions to include in a statistical sample.

The sample size is an important feature of any experimental study where the goal is to draw conclusions about a population from a sample.

Learn more about Sample Size here: brainly.com/question/17203075

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