Question

An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Original digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month. Suppose that you take a sample of 1.100 U.S. adults, what is the probability that fewer than 25 in your sample will watch original digital videos?

a.		0.0179
b.		0.1241
c.		0.25
d.		0.30

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Use the following information to answer the next questions:
Sally Soooie believes University of Arkansas students are more generous than students at other SEC schools and believes that this generosity will lead them to sign up to be organ donors more frequently. She takes a random survey of 100 U of A students (Sample 1) and finds that 78 of them have signed the form to be organ donors. A random sample of students from Vanderbilt (Sample 2) found 62 out of 100 are registered organ donors.
  
1.What is the 90% confidence interval for the proportion of Vanderbilt students that are organ donors based on this sample?

a.		(0.517, 0.715)
b.		(0.487, 0.742)
c.		(0.540, 0.700)
d.		(0.551, 0.685)

2.What would happen to the confidence interval if the professor sampled an additional 100 students to the sample?

a.		It would get wider.
b.		It would become narrower.
c.		It would probably not change.
d.		Sample size does not impact the width of the confidence interval.

Answer 1

The population proportion of success is p = 0.3 , and the sample size is n= 100 . We need to compute

The population mean is computed as:

and the population standard deviation is computed as:

Therefore, we get that

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X	62
Sample Size N	100

The sample proportion is computed as follows, based on the sample size N = 100 and the number of favorable cases X = 62:

The critical value for α=0.1 is z_c = 1.645 . The corresponding confidence interval is computed as shown below:

2.What would happen to the confidence interval if the professor sampled an additional 100 students to the sample?

It would become narrower.