A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet 1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:

a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.

2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).

a. 33
b. 3909
c. 2401
d. 4161

1  

2  

Step-by-step explanation:

From the question we are told that

     The  sample size is  

      The  number of those that said the would use internet is

       The margin of error is  

Generally the sample proportion is mathematically evaluated as

substituting values

substituting values

Generally the standard error of   is mathematically evaluated as

substituting values

For  a  95% confidence interval the confidence level is  95%

Given that the confidence interval is 95% the we can evaluated the level of confidence as

Next we obtain the critical value of   from normal distribution table (reference math dot  armstrong dot edu) , the value is  

Give that the population size is very large  the sample size is mathematically represented as

substituting values  

step-by-step explanation:

where is the questions