# Statistics Example Problems

1. A university wants to estimate the average amount of money that students spend on books in a semester. It takes a random sample of 45 students and finds that the average amount of money spent was $282 with a standard deviation of $21. Find a 95% confidence interval estimate for the true mean amount of money spent on books in a semester.

2. A local public television station, which broadcasts educational programs, is soliciting contributions from its audience during pledge week. The master of ceremonies states that the average contribution of its members is $47. do you think that this average is the mean mode or median? Why?

3. A survey found that 30% of pet owners had their pets bathed professionally rather than doing it themselves. If 18 pet owners are randomly selected find the probability that exactly 5 people have their pets professionally bathed.

4. The Statistical Bulletin published by the Metropolitan life insurance company reported 2% of all Americans birth results in twins. If a random sample of 8000 births is taken, find the mean, variance and standard deviation of the number of births that would result in twins.

5. It was found that 60% of Americans victims of health care fraud are senior citizens. If 10 victims are randomly selected, find the probability that exactly 3 are senior citizens.

6. Find the mean, mode, median, variance and standard deviation of the following data:

35

45

30

35

40

25

7. A survey of 30 adults found that the mean age of a person's primary vehicle is 5.6 years. Assuming the standard deviation of the population is .8 years, find the 95% confidence interval of the population mean.

8. Find everything to the left of Z= 2.42

9. Find everything to the right of Z= -1.68

10. Find everything in between -1.68 and 2.42

© BrainMass Inc. brainmass.com October 10, 2019, 2:56 am ad1c9bdddfhttps://brainmass.com/statistics/quantative-analysis-of-data/statistics-example-problems-400633

#### Solution Preview

1. A university wants to estimate the average amount of money that students spend on books in a semester. It takes a random sample of 45 students and finds that the average amount of money spent was $282 with a standard deviation of $21. Find a 95% confidence interval estimate for the true mean amount of money spent on books in a semester.

CI = xbar +/- z(s/square root n)

Where xbar is the mean, z is the z value from the desired confidence level (1.96 for 95% confidence level) s is the sample standard deviation and n is the sample size.

CI = 282 +/- 1.96(21/square root 21)

= 282 +/- 6.1358

= 275.86 and 288.14

2. A local public television station, which broadcasts educational programs, is soliciting contributions from its audience during pledge week. The master of ceremonies states that the average contribution of its members is $47. do you think that this average is the mean mode or median? Why?

This would be the mean as mean and average have the same definition for general use to the ...

#### Solution Summary

Complete solutions for 10 general statistics problems.