The document discusses the normal distribution and hypothesis testing. It provides characteristics of the normal distribution including its bell shape, mean, and percentages of observations within standard deviations of the mean. It also describes sampling distributions, the central limit theorem, and how the distribution of sample means approaches normality as sample size increases. Finally, it discusses hypothesis testing, including null and alternative hypotheses, types of tests, critical regions, types of errors, and how to test hypotheses about population means.

1. Normal Distribution and Hypothesis Testing STR1K

5. 68.27% 95.45 % 99.73%

8. Example 2 The achievement sores for a college entrance examination are normally distributed with the mean 75 and standard deviation equal to 10. What fraction of the scores would one expect to lie between 70 and 90.

12. N(70, 16)

13. N(70,1)

14. N(70,.25)

16. Example 3 An electrical firm manufactures light bulbs that have a length of life normally distributed with mean and standard deviation equal to 500 and 50 hours respectively. Find the probability that a random sample of 15 bulbs will have an average life ofless than 475 hours.

27. Testing a Hypothesis on the Population Mean Z = X - μ 0 σ /√n t = X - μ 0 S /√n υ = n - 1 H 0 Test Statistic H a Critical Region σ known μ = μ 0 μ < μ 0 μ > μ 0 μ ≠ μ 0 z < -z α z > z α |z| > z α /2 σ unknown μ = μ 0 μ < μ 0 μ > μ 0 μ ≠ μ 0 t < -t α t > t α |t| > t α /2

28. critical value test statistic Reject H 0

29. critical value test statistic Do not reject H 0

30. Example 4 It is claimed that an automobile is driven on the average of less than 25,000 km per year. To test this claim, a random sample of 100 automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 km and a standard deviation of 3,900 km? Use 0.01 level of significance.