Question

1. A medical researcher is interested in the prenatal care received by pregnant women in inner cities. She interviews 20 randomly selected women with children on the streets of Baltimore and finds that the average number of gynecological check ups per pregnancy was 4, with a standard deviation of 1. Using a 95% level of confidence, estimate the population mean number of gynecological visits per pregnancy. Write a concluding statement.

2. An educational researcher sought to estimate the average number of close friends that students on a particular campus made during their first year of school. Questioning a random sample of 50 students completing their freshman year, he finds a sample mean of 4 close friends and a sample standard deviation of 1. Construct a 99% confidence interval to estimate the mean number of close friends made by the population of college students during their first year on campus. Write a concluding statement.

3. An administrator in charge of undergraduate education on a large campus wanted to estimate the average number of books required by instructors. Using bookstore data, she drew a random sample of 15 courses for which she obtained a sample mean of 3.2 books and a sample standard deviation of 0.5. Construct a 99% confidence interval to estimate the mean number of books assigned by instructors on campus. Write a concluding statement.

4. A local police department attempted to estimate the average rate of speed of vehicles along a strip of Main Street. With hidden radar, the speed of a random selection of 35 vehicles was measured, which yielded a sample mean of 45 mph and a standard deviation of 5 mph. Find the 99% confidence interval for the population mean. Write a concluding statement.

5. A researcher examined the extent of cooperation among kindergarten children. She unobtrusively observes a group of children at play for 30 minutes. The following are the number of cooperative acts exhibited by each child. Construct a 95% confidence interval to estimate the population mean of cooperative acts. Write a concluding statement

6. 1

   5

   2

   3

   4

   1

   2

   2

   4

   3

   6. column is for 5

Answer 1

Solution:

1)Given: Standard deviation,s=1

Mean,=4

Sample size,N=20

=0.05(95% confidence level)

• Calculation of standard error of mean.

SE=s/N-1=1/20-1=0.23

• Degree of freedom:Df=N-1=20-1=19
• For =0.05, t=1.73(from the t-distribution table)
• Margin of error=t*SE=1.73*0.23=0.3979
• 95% confidence interval=t*SE

=40.3979

=4.3979 to 3.6021

Thus, we can be 95% certain that the mean number of gynecological visits per pregnancy is between 4.3979 and 3.6021.