1. Assume that the mean age at first marriage among females in in 2003 was 27 yrs old. A random sample of 144 females this year yielded a mean first marriage age of 29.5 with a standard deviation of 4 years. Assume that marriage ages were normally distributed. Is there evidence that the mean first marriage age has increased since 2003? Test the claim at 95% significance level.

a) Null hypothesis

b) Alternate hypothesis

c) P value

d) Conclusion

2. The 77th annual report of the New Mexico department of game and fish stated that the weight of an adult mountain lion is normally distributed. Given that a sample of n=36 adult mountain lions have a mean of 102 lbs and a standard deviation 30.7 lbs construct a 99% confidence interval estimate of population average weight of all adult mountain lions.

3. In an article exploring blood serum levels of vitamins and lung cancer risks in the new England journal of medicine the mean serum level of vitamin E in the control  was 11.2 mg/litre with standard deviation = 4.1. There were 196 patients in the control group. Using this information construct a 90 % confidence interval for the mean serum level of vitamin E in all persons similar to the control.

4). The owner of a local nightclub was recently surveyed a random sample of n=100 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years. What is the p value?