Statistics: 15 Problems

1. A population is normally distributed, with a mean of 23.45 and a standard deviation of 3.8. What is the probability of each of the following?
a. Taking a sample of size 10 and obtaining a sample mean of 22 or more
b. Taking a sample of size 4 and getting a sample mean of more than 26

2. The Statistical Abstract of the United States published by the U. S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviation of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had them keep a record of the fresh fruit they ate for one year.
a. What is the probability that the sample average would be less than 90 pounds?
b. What is the probability that the sample average would be between 93 and 96 pounds?

3. What is the difference between a point estimate and an interval estimate?

4. When do you use the finite correction factor?

5. For a random sample of 36 items and a sample mean of 211, compute a 95% confidence interval for µ if the population standard deviation is 23.

6. Describe when you would use the t distribution instead of the z distribution.

7. What is a degree of freedom?

8. A random sample of 15 items is taken, producing a sample mean of 2.364 with a sample variance of .81. Assume x is normally distributed and construct a 90% confidence interval for the population mean.

9. Write a statistical hypothesis

10. Describe a null and alternative hypothesis

11. What is a critical value

12. What is the relationship between Type I error and alpha

13. Use the data given to test the following hypotheses. Assume the data are normally distributed in the population. H0: µ = 7.48 Ha: µ < 7.48 x = 6.91, n = 24, s = 1.21, a = .01

14. According to a study several years ago by the Personal Communications Industry Association, the average wireless phone user earns $ 62,600 per year. Suppose a researcher believes that the average annual earnings of a wireless phone user are lower now, and he sets up a study in an attempt to prove his theory. He randomly samples 18 wireless phone users and finds out that the average annual salary for this sample is $ 58,974, with a population standard deviation of $ 7,810. Use a = .01 to test the researcher's theory. Assume wages in this industry are normally distributed.

15. A random sample of 51 items is taken, with x = 58.42 and s 2 = 25.68. Use these data to test the following hypotheses, assuming you want to take only a 1% risk of committing a Type I error and that x is normally distributed. H0: µ = 60 Ha: µ < 60