1. A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?

(a) 20% of all adult Americans support the changes. The researcher must ask_______ more American adults. (Round up to the nearest integer.)

(b)25% of all adult Americans support the changes. (b) The researcher must ask _______ more American adults. (Round up to the nearest integer.)'

2.Determine the probability that at least 2 people in a room of 15 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:

(a) Compute the probability that 15 people have different birthdays.

(b) The complement of "15 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 15 share the same birthday.

(a) The probability that 15 people have different birthdays is _____(Round to four decimal places as needed.)

(b) The probability that at least 2 people share a birthday is _____ (Round to four decimal places as needed.)

3. Determine the t-value in each of the cases.

(a) Find the t-value such that the area in the right tail is 0.15 with 20 degrees of freedom. _______(Round to three decimal places as needed.)

(b) Find the t-value such that the area in the right tail is 0.02 with 20 degrees of freedom. _______(Round to three decimal places as needed.)

(c) Find the t-value such that the area left of the t-value is 0.025 with 24 degrees of freedom. [Hint: Use symmetry.]____(Round to three decimal places as needed.)

(d) Find the critical t-value that corresponds to 60% confidence. Assume 23 degrees of freedom.______(Round to three decimal places as needed.)

4. A survey was conducted that asked 1015 people how many books they had read in the past year. Results indicated that x=11.4 books and

s=16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret the interval.

Construct a 95% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete correct choice.

A.There is a 95% probability that the true mean number of books read is between ____ and _____

B. If repeated samples are taken, 95% of them will have a sample mean between ______ here and ______

C.There is 95% confidence that the population mean number of books read is between______ and_____

5. Construct a confidence interval for p1p2 at the given level of confidence. x1=373, n1=549, x2=431, n2=599, 99% confidence

The researchers are _______% confident the difference between the two population proportions, p1p2,

is between______ and ______.

(Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)