Answer:
1.) Proportion of Hollywood movies with genres listed in this period that were comedies = 0.256
2.) The proportion obtained in (1.) is obtained from all the classified movies released in the time period, hence, it is a population proportion.
3.) We should expect a bell shaped curve for the distribution of sample proportions. That is, we expect the distribution to approximate a normal distribution.
4.) The sampling distribution will be centred at the sample proportion of p = 0.256 and mean of np = 12.8.
Step-by-step explanation:
900 total movies came out between 2007 and 2013.
A total of 691 movies are classified into genres. Of that number, 177 are classified as comedy
1.) proportion of Hollywood movies with genres listed in this period that were comedies
P = (number of comedy movies in that period) ÷ (total number of genred movies in that period)
Proportion = P = (177/691) = 0.256
2.) Is this a sample proportion or a population proportion?
A sample proportion is one that describes the fraction of a sample that possess a certain characteristic of interest. It is statistic because it is obtained from and describes the sample.
WHILE
A population proportion is one that describes the fraction of a population that possess the characteristic of interest. It is a parameter as it is obtained from and describes the entire population.
The proportion obtained in (1.) is obtained from all the classified movies released in the time period, hence, it is a population proportion.
If a random sample of classified movies were selected and the proportion evaluated, then, it could be a sample proportion, but, this one uses every classified movie released in between 2007 and 2013 to arrive at that proportion for comedy movies.
3.) If we took many samples of size 50 from the population of all Hollywood movies with genres listed from this period and recorded the proportion of comedies for each sample, what shape do we expect the distribution of sample proportions to have?
For a distribution of proportion for different sample sizes to approximate a normal distribution and have a bell shape curve, it must satisfy the two conditions,
Some texts use
np > 5 and n(1-p) > 5
and others use
np ≥ 10 and np(1-p) ≥ 10
where n = sample size = 50
p = proportion = 0.256
np = (50)(0.256) = 12.8 > 5
n(1-p) = (50)(0.744) = 37.2 > 5
Note that np = 12.8 ≥ 10
But, np(1-p) = (50)(0.256)(1-0.256) = 9.53 < 10
With how close np(1-p) is to 10, it is still safe to approximate this distribution to a normal distribution. Especially because the entire distribution for the population, completely satisfies all the conditions.
Hence, we expect a bell shaped curve for the distribution of sample proportions. That is, we expect the distribution to approximate a normal distribution.
4.) Where do we expect the sampling distribution from part (3) to be centered?
The sample proportion will always range around the population proportion without bias.
So, the sampling distribution will be centred at the sample proportion of p = 0.256 and mean of np = 12.8.
Hope this Helps!!!
